著色問題(graph coloring problem)的研究已行之有年，並衍生出廣泛的實際應用，但還缺乏一般化的著色問題模型。本論文建構一般化的著色問題模型，其目標函數包含顏色成本的固定支出和點著色變動成本。此著色模型為0/1整數線性規畫模型，其限制式含有選點問題(node packing problem)的限制式。我們利用圖中的極大團(maximal clique)所構成的強力限制式，取代原有的選點限制式，縮短求解時間。我們更進一步舉出一個特殊指派問題並將此著色模型應用於此指派問題上。本論文亦針對此指派問題發展了一個演算法來尋找極大團。計算結果顯示極大團限制式對於此著色問題模型的求解有極大的效益。 / The graph coloring problem (GCP) has been studied for a long time and it has a wide variety of applications. A straightforward formulation of graph coloring problem has not been formulated yet. In this paper, we formulate a general GCP model that concerns setup cost and variable cost of different colors. The resulting model is an integer program that involves the packing constraint. The packing constraint in the GCP model can be replaced by the maximal clique constraint in order to shorten the solution time. A special assignment problem is presented which essentially is a GCP model application. An algorithm of finding maximal cliques for this assignment problem is developed. The computational results show the efficiency of maximal clique constraints for the GCP problem.

Dans cette thèse, nous nous intéressons à l'étude de trois équations aux dérivées partielles et d'évolution non-locales en espace et en temps. Les solutions de ces trois solutions peuvent exploser en temps fini. Dans une première partie de cette thèse, nous considérons l'équation de la chaleur nonlinéaire avec une puissance fractionnaire du laplacien, et obtenons notamment que, dans le cas d'exposant sur-critique, le comportement asymptotique de la solution lorsque $t\rightarrow+\infty$ est déterminé par le terme de diffusion anormale. D'autre part, dans le cas d'exposant sous-critique, l'effet du terme non-linéaire domine. Dans une deuxième partie, nous étudions une équation parabolique avec le laplacien fractionnaire et un terme non-linéaire et non-local en temps. On montre que la solution est globale dans le cas sur-critique pour toute donnée initiale ayant une mesure assez petite, tandis que dans le cas sous-critique, on montre que la solution explose en temps fini $T_{\max}>0$ pour toute condition initiale positive et non-triviale. Dans ce dernier cas, on cherche le comportement de la norme $L^1$ de la solution en précisant le taux d'explosion lorsque $t$ s'approche du temps d'explosion $T_{\max}.$ Nous cherchons encore les conditions nécessaires à l'existence locale et globale de la solution. Une toisième partie est consacré à une généralisation de la deuxième partie au cas de systèmes $2\times 2$ avec le laplacien ordinaire. On étudie l'existence locale de la solution ainsi qu'un résultat sur l'explosion de la solution avec les mêmes propriétés étudiées dans le troisième chapitre. Dans la dernière partie, nous étudions une équation hyperbolique dans $\mathbb{R}^N,$ pour tout $N\geq2,$ avec un terme non-linéaire non-local en temps. Nous obtenons un résultat d'existence locale de la solution sous des conditions restrictives sur les données initiales, la dimension de l'espace et les exposants du terme non-linéaire. De plus on obtient, sous certaines conditions sur les exposants, que la solution explose en temps fini, pour toute condition initiale ayant de moyenne strictement positive.

L'avènement du numérique permet de stocker de grandes quantités de parole à moindre coût. Malgré les récentes avancées en recherche documentaire audio, il reste difficile d'exploiter les documents à cause du temps nécessaire pour les écouter. Nous tentons d'atténuer cet inconvénient en produisant un résumé automatique parlé à partir des informations les plus importantes. Pour y parvenir, une méthode de résumé par extraction est appliquée au contenu parlé, transcrit et structuré automatiquement. La transcription enrichie est réalisée grâce aux outils Speeral et Alize développés au LIA. Nous complétons cette chaîne de structuration par une segmentation en phrases et une détection des entités nommées, deux caractéristiques importantes pour le résumé par extraction. La méthode de résumé proposée prend en compte les contraintes imposées par des données audio et par des interactions avec l'utilisateur. De plus, cette méthode intègre une projection dans un espace pseudo-sémantique des phrases. Les différents modules mis en place aboutissent à un démonstrateur complet facilitant l'étude des interactions avec l'utilisateur. En l'absence de données d'évaluation sur la parole, la méthode de résumé est évaluée sur le texte lors de la campagne DUC 2006. Nous simulons l'impact d'un contenu parlé en dégradant artificiellement les données de cette même campagne. Enfin, l'ensemble de la chaîne de traitement est mise en œuvre au sein d'un démonstrateur facilitant l'accès aux émissions radiophoniques de la campagne ESTER. Nous proposons, dans le cadre de ce démonstrateur, une frise chronologique interactive complémentaire au résumé parlé.

<p>This report is written on commission by WSP Acoustics. The report studies the outdoor sound levels on school yards in Stockholm. The questions given by the company to be answered was what are the actual sound levels at diffrent school yards with low traffic noise and how can you construct a facade element that reduces the sound level from the outside and meet the indoor requirements. Mesurements for four hours was done at eight schools set north and south of the city centre. The measurement period included one school break and one lunch break. The results of the measurements were that the equivalent and maximum sound level had small variations between the schools with some exceptions.The equivalent sound level was Leq 58-62 dB(A) and this shows a small variation. The school with the highest equivalent sound level of 67 dB was Maria skolan. This high level can be explained by more children on the school yard together at the same time etc. The maximum sound level was 85-89 dB(A), this if the level for Sofia skolan 82 dB was ignored. The level 85-89 dB(A) also shows a small variation. Calculations of the sound reduction index (R'w) for facade elements were also carried out for all the schools. The resulting sound reduction index for the whole facade was 34-41 dB. After assuming a 200 mm thick concrete facade for Sjöstadsskolan another calculation of building elements gives that the window have to reduce R'w 32 dB to meet the indoor requirements. In the future WSP Acoustics will use this report to choose building elements such as windows when building or rebuilding schools. It can also be used if any of the eight schools in this report needs a window changed to improve the acoustics.</p>

This report is written on commission by WSP Acoustics. The report studies the outdoor sound levels on school yards in Stockholm. The questions given by the company to be answered was what are the actual sound levels at diffrent school yards with low traffic noise and how can you construct a facade element that reduces the sound level from the outside and meet the indoor requirements. Mesurements for four hours was done at eight schools set north and south of the city centre. The measurement period included one school break and one lunch break. The results of the measurements were that the equivalent and maximum sound level had small variations between the schools with some exceptions.The equivalent sound level was Leq 58-62 dB(A) and this shows a small variation. The school with the highest equivalent sound level of 67 dB was Maria skolan. This high level can be explained by more children on the school yard together at the same time etc. The maximum sound level was 85-89 dB(A), this if the level for Sofia skolan 82 dB was ignored. The level 85-89 dB(A) also shows a small variation. Calculations of the sound reduction index (R'w) for facade elements were also carried out for all the schools. The resulting sound reduction index for the whole facade was 34-41 dB. After assuming a 200 mm thick concrete facade for Sjöstadsskolan another calculation of building elements gives that the window have to reduce R'w 32 dB to meet the indoor requirements. In the future WSP Acoustics will use this report to choose building elements such as windows when building or rebuilding schools. It can also be used if any of the eight schools in this report needs a window changed to improve the acoustics.

Syfte och frågeställningar Syftet med studien var att undersöka för elitorienterare resultaten vid och korrelationen mellan ett så kallat 5 minuters pyramidtest (5MPT) och ett maximalt test för bestämning av maximalt syreupptag (VO2max) på rullband. Frågorna vi ställde oss var: Vilken korrelation föreligger mellan 5MPT och ett bestämt VO2max på rullband hos elitorienterare? Hur ser en jämförelse ut mellan uppmätt samt beräknat VO2max? Vilken är reliabiliteten för 5MPT? Hur ser ekvationen ut för att beskriva sambandet mellan dessa två olika maxtester? Metod I valideringsstudien deltog 16 elitorienterare (6 kvinnor och 10 män) i åldrarna 17 till 37 år. De två testerna som genomfördes var 5MPT och bestämning av VO2max på rullband. 5MPT är ett skytteltest som är fem minuter långt, där testpersonen (tp) tar sig fram och tillbaka mellan två stolpar (sträcka 5.5 m) där en vertikal trappa (formad likt en pyramid) passeras under varje vända. Antalet vändor, skattad ansträngning samt hjärtfrekvens (HF) registrerades. Utvecklad power (effekt) erhölls genom produkten av vikt, gravitation, antal vändor, höjd på högsta plinten (0,62 m) dividerat med total duration i 5MPT. Testet för att bestämma VO2max utfördes med löpning på ett motordrivet rullband. Under den första minuten av testet sprang tp på en hastighet av 8km/h (kvinnor) respektive10km/h (män) utan lutning. För varje minut ökades hastigheten med 1km/h. Lutningen höjdes med en grad efter minut ett och därefter med 0,5 grader/minut. Testet pågick till dess tp nått sin VO2max. Var 15:e sekund registrerades tp:s HF, VO2 (l/min), VCO2 (l/min), VO2 (ml/kg/min) och respiratorisk kvot (RER) med hjälp av ett datoriserat syreupptagningssystem. Resultat Korrelationen var signifikant och hög (r = 0,89, p&lt;0,0001) mellan utvecklad power på 5MPT och VO2max (l/min) och även mellan antalet vändor på 5MPT och VO2max (l/min) (r = 0,89, p&lt;0,0001) på detta material av elitorienterare. Följande formler, baserade på resultaten från elitorienterarna, kan användas för att predicera VO2max efter genomfört 5MPT: VO2max  (l/min) = (5MPTPOWER – 50,914) / 25,795 VO2max (l/min) = (5MPTVÄNDOR – 74,447) / 9,7668 Slutsats 5MPT uppvisar en stark korrelation med bestämd VO2max sett till power och/eller antalet genomförda vändor. Beräkningsformler för prediktion av VO2max har varit möjligt att beskriva. Se resultatdelen för andra resultat och samband mellan 5MPT och VO2max. / Abstract Aim The aim of this study was to investigate for elite orienteers the results in and the correlation between a so called 5-minutes-pyramid test (5MPT) and a specific maximum oxygen uptake test (VO2max) on a treadmill. The questions we asked ourselves were: Which correlation exists between 5MPT and a specific VO2max on the treadmill for elite orienteers? How would a comparison look like between measured and estimated VO2max? What is the reliability for the 5MPT? How would an equation look like that describe the correlation above? Method In the validity the study 16 elite orienteers (6 women and 10 men) aged 17 to 37 years participated. The two tests that have been carried out were the 5MPT and determined VO2max during running on a treadmill. The 5MPT is a 5-minute-shuttle test, in which the participant moves back and forth in a short interval (5.5 m) over boxes (highest height: 0.62) formed like a pyramid. Power in the pyramid test (5MPTPOWER) was calculated as the product of numbers of laps, body weight, gravity and highest box level divided by time. To determine VO2max the method running on a treadmill was performed. During the first minute the running speed was 8km/h (women)/10 km/h (men) without elevation. Each minute the velocity increased with 1 km/h. The elevation increased with 1 degree after the first minute and thereafter with 0,5 degrees/minute.  The test was finished when the participant had reached her VO2max. Every 15 second the participants heart rate, VO2 (l/min), VCO2 (l/min), VO2 (ml/kg/min) and RER, was registered by means of an online system. Results The correlation between the developed power of the 5MPT and measured VO2max (l/min) was high (r = 0.89, p&lt;0,0001) and also between the number of laps in the 5MPT and measured VO2max (l/min) (r = 0.89, p &lt; 0,0001). The following formulas can be used to predict VO2max after completed 5MPT: VO2max  (l/min) = (5MPTPOWER – 50,914) / 25,795 VO2max (l/min) = (5MPTLAPS – 74,447) / 9,7668 Conclusions 5MPT show a strong correlation with VO2max determined in terms of power and/or the number of completed laps. Calculated formulas for prediction of VO2max have been possible to describe. See results section for other results and relationships between 5MPT and VO2max. / Maximal Aerobic Power versus Performance in Two Aerobic Endurance Tests among Young and Old Adults.Andersson E, Lundahl N, Wecke L, Lindblom I, Nilsson, J.

Multi-user MIMO (MIMO-MU) communication techniques make use of available channel state information at the transmitter to mitigate the inter-user interference. The goal of these techniques is to provide the least interference at the mobile stations by applying a precoding operation. In this thesis a comparison of available techniques in the literature such as Channel Decomposition, SINR Balancing, Joint-MMSE optimization is presented. Novel techniques for the MIMO multi-user downlink communication systems, where a single stream is transmitted to each user are proposed. The proposed methods, different from the other methods in the literature, use a simple receiver to combat the interference. It has been shown that MRC based receivers are as good as more complicated joint MMSE receivers.

Materials when subjected to deformation exhibit unstable plastic flow beyond the elastic limit. In certain range of temperature and strain rates many solid state solutions, both interstitial as well as substitutional, exhibit the phenomenon of serrated yielding which also goes by the name, the Portevin - Le Chatelier (PLC) effect. The origin of this plastic instability is due to the interaction of dislocations with solute atoms. The objective of the thesis is to provide a dynamical systems approach to the study of this plastic flow instability. The thesis work discusses, within the framework of a model, the connection between microscopic dislocation mechanisms and macroscopic mechanical response of the specimen as stress drops in stress-strain curves. An extension of the model to the associated deformation bands is also considered. The emphasis is on the dynamical aspects of the instability. The methods of nonlinear dynamics like geometrical slow manifold and Poincare map formalism are applied for the first time to study the PLC effect. However, the approach and techniques transcend this particular application as the techniques are equally well applicable for many other physical systems as well, in particular, systems involving multiple time scales. The material covered should be of interest to investigators in the materials science, in particular, those, involved in the dislocation patterning and self organization of dislocations. Many theoretical models for the PLC effect exist in literature. Although the physical phenomenon is inherently dynamic, the conventional theoretical models do not involve any dynamical aspect. A dynamical model for this effect, due to Ananthakrishna, Sahoo and Valsakumar provides an explanation in terms of the dynamic interactions between different dislocation species and evolution of densities of these dislocation species. This model is known to reproduce several of the experimental results. It is within the perspective of this model and its extensions we analyze the PLC effect. The macroscopic manifestation of the PLC effect is the repeated load drops or serration in stress-strain curves (beyond the yield point). Each of the load drop is associated with the formation of a spatial dislocation band and its subsequent propagation. From the perspective of a dynamical system, the changeover from the stress-strain curve with single yield drop to repeated yield drops (the PLC effect) corresponds to a Hopf bifurcation wherein equilibrium state changes over to a periodic steady state. These repeated load drops correspond to auto oscillations of the applied stress (in the absence of any periodic driving force). In particular, as implied by the slow loading and sudden load drops, these oscillations are classified as relaxation oscillations. Relaxation oscillations are a result of disparate time scales of dynamics of the participating modes. Within the context of the model, this refers to very different time scales of evolution of densities of mobile (fast), immobile (slow) dislocations and those with a cloud of solute atoms (not too slow). The focus of attention in the thesis work is on these auto relaxation oscillations. There are several methodologies in nonlinear dynamical systems to study the oscillatory behavior of multidimensional systems with multiple time scales. An effective way is to study the reduced dynamical system in an appropriate space without sacrificing the required dynamical information. To this end, we discuss two techniques which compliment each other. 1.Slow manifold approach: This method utilizes the presence of multiple time scales dynamics. Advantage is that the information on the nature of evolution of the periodic orbit is retained. The limitation is that the transition from one stable state to another as parameter is varied cannot be dealt with. 2.Poincare maps:This approach utilizes the recurrent behavior of the period orbit. This is a convenient methodology to study the nature of stability of periodic orbits. However, in this, the information about the nature of evolution is lost. Both the above techniques provide good description in the presence of high dissipation or larger separation of time scales of the participating modes. For slow manifold analysis, this leads to exact slow manifold structure while in the case of Poincare maps, it leads to simpler, lower dimensional attractors. Specific issues that are dealt with using these approaches and others in this thesis are the following. To start with, we first provide a comprehensive overview of the dynamical behavior as envisaged by the model system in physically relevant two parameter space. The existence of relaxation oscillations bounded by back-to-back Hopf bifurcation is a good representation of the fact that the PLC effect manifests only in a window of strain rates. Within this boundary of Hopf bifurcations relaxation oscillations destabilize to give rise to new states of order, including the chaotic states. The changes in the nature of these oscillations with control parameters is projected through the bifurcation diagrams and analyzed using techniques like Floquet multipliers, Lyapunovs exponents etc. After the identification of the relevant parameter space for the monoperiodic relaxation oscillations, we focus our attention on the time scales involved in these relaxation oscillations and its connection to the time scales apparent in serrations of the stress-strain curve of the PLC effect. This characteristic feature of the PLC effect, the stick-slip nature of stress-strain curves, is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to arise from a competition of the relevant time scales involved in the phenomenon. However, in the previous works, the identification and the role of the time scales in the dynamical phenomenon is not clear. The motivation of this part of the work is to identify the time scales involved in the stress drops of the time series and their origin. Since the dynamics involves distinct time scales, in the long time limit, the evolution is controlled only by the slow modes. Hence, the adiabatic elimination or quasi-steady state approximation of the fast modes leads to an invariant manifold, the slow manifold which is useful for the analysis of time scales. The geometry of the slow manifold which is atypical with two connected pieces is shown to be at the root of the relaxation oscillations. The analysis of the slow manifold structure helps to understand the time scales of the dynamics operating in different regions of the slow manifold. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity of the flow stress. The slow-fast dynamical nature manifests itself through multiperiodic oscillations also, in the form of mixed mode oscillations (MMOs), which are oscillations with both large amplitude excursions as well as small amplitude loops. In MMOs, the small amplitude oscillatory loops are confined to one part of the slow manifold (around the fixed point) and the large amplitude excursions arise as jumps from one piece of the slow manifold to the other. More generally, MMOs are a characteristic feature of a family of dynamical systems which also exhibit alternate periodic-chaotic sequences in bifurcation portraits. Usually, the origin of these features is explained in terms of either the approach to a homoclinic bifurcation duo to a saddle fixed point (Shilnikov scenario) or a saddle orbit (Gavrilov-Shilnikov scenario). However, the dynamical model exhibits features from both the above scenarios. The emphasis of this study is on explaining the origin of the incomplete approach to a global bifurcation in the dynamical model. Apart from attempting to understand the complex bifurcation sequences, an additional motivation for this study is the apparent lack of systematic investigation into the incomplete approach to global bifurcation exhibited by a variety of physical systems. The method of the analysis is general and applicable to the family of MMO systems. In the model, using the structure of the bifurcation sequences, and the equilibrium fixed point, a local analysis shows that the approach to homoclinicity is asymptotic at best, and is a result of the ‘softening' of eigenvalues of the saddle equilibrium point. This softening, in turn, is a consequence of back-to-back Hopf bifurcation which reflects the constraint of the physical phenomenon, namely, the occurrence of the multiple stress drops only in an interval of the strain rates. The characteristic features, namely, MMOs, alternate periodic-chaotic sequences, and incomplete approach to homoclinicity are related to each other and arise as a consequence of the atypical slow manifold structure. The slow manifold structure analysis assumes that the evolution of the system is constrained within the neighborhood of the slow manifold which also implies that the dynamical system involves high dissipation. Hence, the dimension of the effective dynamics in the long time limit is reduced. The analysis reveals information regarding the structure of the periodic orbit for a given set of parameter values but does not provide any information regarding the nature of stability of the periodic orbits. However, any insight into the mechanism of the instability of the periodic orbits in the model may lead to a better understanding of the underlying physical phenomenon. Poincare maps and equivalent discrete dynamical systems provide a convenient means to obtain such an insight on the nature of the periodic solutions of the dynamical system. This methodology compliments the invariant slow manifold analysis, since in Poincare maps, the nature of the stability information is preserved at the expense of the structure of the periodic orbit. However, these two methodologies are not exclusive to each other, since the slow manifold structure as well as Poincare maps may be constructed using a common factor, namely, extremal values of the fast variable of the dynamical system. The methodologies adopted for the analysis assumes large dissipation arising out of the multiple time scale behavior such that the next maximal amplitude (NMA) maps can be modeled by one dimensional discrete dynamical systems. The dynamical portrait of the model shows differing nature of dynamics and consequently Poincare maps with different geometrical shapes in the {m,c) plane. Within the framework of one dimensional maps, these shapes can be schematically reconstructed using minimal information regarding the principal periodic orbit embedded in higher dimension and its nature of stability. This suggests that one dimensional maps might be sufficient to represent the higher dimensional dynamical system. For most of the parameter space, the NMA maps of the dynamical model possess characteristic features of a locally smooth maximum and asymptotically long tail. These features have been observed in many other physical systems, both experimental and model systems. Hence, this analysis is focused on a broader issue of Poincare maps in a family of dynamical systems with multiple time scale dynamics and mixed mode oscillations. Here, the dynamical model has been used as a representative dynamical system for this family. The scope of the study is to understand the dynamical features of the MMO systems within the framework of one dimensional systems. Specifically, by using some general constraints on the one dimensional map, we first analyze the basic mechanism that is responsible for the reversal of periodic sequences of RLk type which corresponds to the dominant periodic states of the MMO systems. This in turn allows us to understand the period adding sequences as well. The analysis also helps to demonstrate that the width of the periodic states contained within the chaotic regions bounded by two successive periodic states of the form RLk is smaller than that for RLk .To this end, we first construct a model map which mimics the dominant bifurcation sequences of MMO systems. This map is utilized to verify the analytical results for the parameter width of the periodic windows. This analysis also throws light on the origin of the ordered structure of the isolas of RLk periodic orbits, in MMO systems, which was shown to be the result of a back-to-back Hopf bifurcation. The results indicate the ubiquity in the qualitative dynamical features of physical systems from widely differing origin, exhibiting alternate periodic-chaotic sequences. Although the model for the PLC effect is successful in describing the features of the phenomenon, a shortcoming of the dynamical model has been the absence of the spatial aspect. A dominant process in the PLC effect is the movement of dislocations (mainly through cross glide) which is essentially nonlocal. This feature has been incorporated into the dynamical model through a 'diffusive' term for the mobile dislocations. Preliminary results indicate that various types of band propagation, as seen in experiments, are recovered. It is known that the solute atmosphere aggregation occurs primarily during the waiting time of the mobile dislocations after its arrest. As another extension, the present model has been revised to incorporate these aging effects also. An outline of the thesis is as follows. Focus of this thesis work is on the dynamical aspects of the PLC effect. The phenomenology and few techniques in nonlinear dynamics are introduced in Chapters 1 and 2. Chapter 3 provides a comprehensive tour of dynamical behavior of the model in physically relevant two-parameter space. The rest of the work is presented in three parts (six chapters). In the first part of the thesis, the structure of the relaxation oscillations in the phase space is analyzed using the topology of the slow manifold. A connection between the slow manifold structure and the negative strain rate sensitivity of the flow stress is attempted using this analysis (Chapter 4). As a natural extension, the approach is utilized for the analysis of multiperiodic relaxation oscillations also. The emphasis is on the connection between the dynamical behavior of the model and incomplete approach to a global bifurcation (Chapter 5). In the second part of the thesis, the stability properties of periodic orbits are analyzed in detail using the Poincare map formalism, complimenting the study on the structure of periodic orbits using slow manifold. The structure and gross features of the Poincare map are reproduced utilizing only minimum information regarding the principal periodic orbit in the multidimensional space (Chapter 6). Within the framework of one dimensional systems, we analyze the mechanisms responsible for the structure of bifurcation portraits of MMO systems (Chapter 7). Third and the last part, of work focuses on modeling the spatial aspect of the PLC effect and refinement of the dynamical model (Chapters). The last chapter, Chapter9, is devoted for discussion of the results and scope for future work.

Le sujet de cette thèse se situe à la frontière entre les mathématiques appliquées et la mécanique. Il s'agit d'étudier, sous un angle mathématique, des problèmes piézoélectriques, c'est à dire des problèmes couplant action mécanique et action électrique, en présence de contact et de frottement. On s'intéresse notamment à l'analyse variationnelle et numérique de ces problèmes. La thèse comporte quatre parties. La première partie contient l'ensemble des outils mathématiques, numériques et mécaniques nécessaires à une bonne compréhension du travail réalisé par la suite. La deuxième partie aborde deux problèmes statiques de contact frottant entre un corps électro-élastique et une fondation. Dans le cas des formulations primales des problèmes, nous prouvons l'existence, l'unicité, et la dépendance continue des solutions faibles, exprimées en termes de déplacements et de potentiel électrique. Une formulation duale équivalente au problème précédent, exprimée en termes de contraintes et de déplacement électrique, est étudiée pour laquelle des résultats d'existence et d'unicité sont établis. La troisième partie aborde deux modèles de contact piézoélectrique dans un cadre évolutif de type quasistatique. Pour chaque modèle, on présente un résultat d'existence. Dans la quatrième partie, le travail porte sur l'analyse numérique et les simulations par différences finies en temps (Euler implicite) et éléments finis en espace. Dans le cas statique, on traite un problème électro-élastique avec contact frottant de type compliance. Le problème discret est posé et les estimations a priori de l'erreur sont obtenues. Le problème est écrit sous forme d'un Lagrangien augmenté couplé à un algorithme de type Newton généralisé. S'ensuit une simulation numérique en dimension deux d'espace et des vérifications numériques de convergence. Des résultats similaires sont obtenus dans le cas d'un problème de contact quasistatique électro-viscoélastique.

Cette thèse est consacrée à la résolution de trois types de problèmes fondamentaux qui apparaissent en analyse fonctionnelle hilbertienne non-linéaire et dans ses applications : les problèmes d'équilibre pour les bifonctions monotones, les problèmes de point fixe pour les contractions, et les problèmes d'inclusion pour les opérateurs monotones. Notre objectif est d'élaborer de nouvelles méthodes d'approximation et de construction de solutions pour ces problèmes et d'étudier leur comportement asymptotique. Dans un premier temps, nous proposons de nouvelles perturbations visqueuses et visco-pénalisées de ces problèmes, et étudions le comportement asymptotique des courbes d'approximation associées quand la perturbation devient évanescente. Nous étudions ensuite les propriétés de divers systèmes dynamiques discrets et continus associés à ces courbes. Cette étude débouche en particulier sur de nouveaux algorithmes, dont la convergence est établie. Des applications numériques à des problèmes de restauration en traitement de l'image sont fournies pour illustrer la mise en œuvre et les performances de certains des algorithmes proposés.