On s’intéresse dans cette thèse à montrer que la solution approchée, par la méthode des volumes finis, converge vers la solution renormalisée de problèmes elliptiques ou paraboliques à donnée L1. Dans la première partie nous étudions une équation de convection-diffusion ellliptique à donnée L1. En adaptant la stratégie développée pour les solutions renormaliséesà la méthode des volumes finis, nous montrons que la solution approchée converge vers l’unique solution renormalisée.Dans la deuxième partie nous nous intéressons à un problème parabolique nonlinéaire à donnée L1. En utilisant une version discrète de résultats de compacité classiques, nous montrons que les résultats obtenues dans le cas elliptique restentvrais dans le cas parabolique. Dans la troisième partie nous montrons des résultats similaires pour une équationparabolique doublement non-linéaire à donnée L1. Le caractère doublement nonlinéaire de l’équation crée des difficultés supplémentaires par rapport à la partie précédente, notamment car la règle de dérivation en chaîne ne s’applique pas dansle cas discret. Enfin, dans la quatrième partie, nous utilisons les résultats établis précédemment pour étudier un système de type thermoviscoélasticité. Nous montrons que la solution approchée, obtenue par un schéma éléments finis-volumes finis, converge vers une solution faible-renormalisée du système. / In this thesis we are interested in proving that the approximate solution, obtained by the finite volume method, converges to the unique renormalized solution of elliptic and parabolic equations with L1 data. In the first part we study an elliptic convection-diffusion equation with L1 data. Mixing the strategy developed for renormalized solution and the finite volume method,we prove that the approximate solution converges to the unique renormalized solution. In the second part we investigate a nonlinear parabolic equation with L1 data. Using a discrete version of classical compactness results, we show that the results obtaines previously in the elliptic case hold true in the parabolic case. In the third part we prove similar results for a doubly nonlinear parabolic equation with L1 data. The doubly nonlinear character of the equation makes new difficulties with respect to the previous part, especially since the chain rule formula does not apply in the discrete case. Finaly, in the fourth part we use the results established previously to investigate a system of thermoviscoelasticity kind. We show that the approximate solution,obtaines by finite element-finite volume scheme, converges to a weak-renormalized solution of the system.

<p>Cilj&nbsp; ovog&nbsp; rada&nbsp; bio&nbsp; je&nbsp; ispitivanje&nbsp; mogućnosti&nbsp; primene&nbsp; modifikovanog&nbsp; bentonita&nbsp; kao katalizatora&nbsp; (ferioksalat&nbsp; i&nbsp; Al,&nbsp; Fe-bentonit&nbsp; katalizatori)&nbsp; u&nbsp; Fenton&nbsp; i&nbsp; foto-Fenton&nbsp; procesu&nbsp; uklanjanja tekstilne&nbsp; reaktivne&nbsp; boje&nbsp; Reactive&nbsp; Red&nbsp; 120.&nbsp; Do&nbsp; sada&nbsp; su&nbsp; objavljene&nbsp; studije&nbsp; primene&nbsp; heterogenog Fenton procesa sa različitim koncentracijama gvožđau katalizatorima i sa kompleksom ferioksalata,međutim, njihovo poređenje u smislu efikasnosti obezbojavanja nije istraženo, &scaron;to je bio jedan od fokusa&nbsp; istraživanja&nbsp; u&nbsp; ovom&nbsp; radu.&nbsp; Osim&nbsp; toga,&nbsp; potencijal&nbsp; sunčeve&nbsp; energije&nbsp; predstavlja&nbsp; 16,7%&nbsp; od ukupno&nbsp; iskoristivog&nbsp; potencijala&nbsp; obnovljivih&nbsp; izvora&nbsp; energije&nbsp; u&nbsp; Srbiji,&nbsp; dok&nbsp; je&nbsp; prosečno&nbsp; sunčevo zračenje&nbsp; u&nbsp; Srbiji&nbsp; oko&nbsp; 40%&nbsp; vi&scaron;e&nbsp; od&nbsp; evropskog&nbsp; proseka,&nbsp; čineći&nbsp; ga&nbsp; vrlo&nbsp; zanimljivim&nbsp; za&nbsp; primenu&nbsp; u ovom tipu tretmana. U cilju &scaron;to boljeg iskori&scaron;ćenjasunčevog zračenja i unapređenja fotokatalitičkih performansi&nbsp; procesa&nbsp; primenjen&nbsp; je&nbsp; parabolični&nbsp; koncentri&scaron;ući&nbsp; reaktor,&nbsp; koji&nbsp; je&nbsp; za&nbsp; ovu&nbsp; vrstu&nbsp; procesa prvi put upotrebljavan. Proučavano je u kojoj meri je solarna fotokataliza značajan segment tehnike za tretman otpadnih voda tokom degradacije perzistentnih jedinjenja, kao &scaron;to je organska azo boja. Takođe, utvrđen je i potencijal fotolize vodonik-peroksida za obezbojavanjem sintetičkog rastvora date&nbsp; boje.&nbsp; Prva&nbsp; faza&nbsp; imala&nbsp; je&nbsp; za&nbsp; cilj&nbsp; sintezu&nbsp; materijala&nbsp; primenom&nbsp; različitih&nbsp; metoda&nbsp; pripreme&nbsp; i<br />konstrukciju solarnog paraboličnog reaktora, koji će se koristiti u Fenton i foto-Fenton procesima degradacije boje Reactive Red 120. Druga faza je podrazumevala karakterizaciju novosintetisanih materijala i optimizaciju procesa fotokatalize primenom Fenton i foto-Fenton procesa i određivanje postignutih efikasnosti primenjenih procesa. Takođe, vr&scaron;eno je određivanje stepena mineralizacije i identifikacija degradacionih produkata nakon procesa degradacije tekstilne boje Reactive Red 120, kao&nbsp; i&nbsp; primena&nbsp; foto-Fenton&nbsp; procesa&nbsp; na&nbsp; realnom&nbsp; efluentu.&nbsp; Na&nbsp; osnovu&nbsp; dobijenih&nbsp; rezultata&nbsp; tokom primene Fenton procesa i kori&scaron;ćenjem oba tipa katalizatora u periodima niskog i visokog intenziteta zračenja,&nbsp; sa&nbsp; aspekta&nbsp; postizanja&nbsp; visoke&nbsp; efikasnosti&nbsp; obezbojavanja&nbsp; i&nbsp; najmanjeg&nbsp; izluživanja&nbsp; gvožđa,<br />može&nbsp; se&nbsp; zaključiti&nbsp; da&nbsp; je&nbsp; Fenton&nbsp; proces&nbsp; najefikasniji&nbsp; na&nbsp; pH&nbsp; vrednosti&nbsp; 3.&nbsp; AlFeB&nbsp; je&nbsp; pokazao&nbsp; veću reaktivnost čak i pri manje upotrebljenim dozama od0,05 g u odnosu na CuOFeB (0,2 g), kao i mogućnost&nbsp; manje&nbsp; upotrebe&nbsp; vodonik-peroksida&nbsp; od&nbsp; 2,5&nbsp; mM,&nbsp; za&nbsp; postizanje&nbsp; visoke&nbsp; efikasnosti obezbojavanja i postignut visok stepen mineralizacije. Vi&scaron;i intenzitet sunčevog zračenja omogućava odvijanje reakcije obezbojavanja na vi&scaron;im pH vrednostima primenom oba katalizatora tokom fotoFenton&nbsp; procesa.&nbsp; Ovo&nbsp; je&nbsp; posebno&nbsp; izraženo&nbsp; kod&nbsp; CuOFeB&nbsp; tokom&nbsp; letnjeg&nbsp; perioda&nbsp; (pH&nbsp; 7),&nbsp; čak&nbsp; i&nbsp; pri nižim dozama katalizatora. Međutim, najveći udeo u&nbsp; procesu obezbojavanja pri upotrebi CuOFeB katalizatora ima fotoliza vodonik-peroksida (80%). Suprotno ovim rezultatima, pri istim reakcionim uslovima,&nbsp; potrebna&nbsp; je&nbsp; veća&nbsp; količina&nbsp; AlFeB&nbsp; katalizatora&nbsp; (0,1&nbsp; g)&nbsp; i&nbsp; niža&nbsp; pH&nbsp; vrednost&nbsp; reakcije,&nbsp; a efikasnost&nbsp; procesa&nbsp; značajno&nbsp; zavisi&nbsp; od&nbsp; početne&nbsp; koncentracije&nbsp; H₂O₂.&nbsp; Činjenica&nbsp; da&nbsp; se&nbsp; u&nbsp; pripremi katalizatora koristio bentonit kao prirodan, &scaron;irokorasprostranjen i jeftin materijal i solarno zračenje kao obnovljiv i alternativni izvor fotona, gore navedene rezultate bi trebalo uzeti u obzir prilikom analize tro&scaron;kova efikasnosti primenjenog procesa. Takođe, primena unapređenih procesa oksidacije se&nbsp; razmatra&nbsp; kao&nbsp; predlog&nbsp; za&nbsp; najbolju&nbsp; dostupnu&nbsp; tehniku&nbsp; kada&nbsp; je&nbsp; u&nbsp; pitanju&nbsp; tretman&nbsp; otpadne&nbsp; vode tekstilne industrije, dok se kao dodatne nove tehnike uzimaju u obzir foto-oksidacije i ispitivanje mogućnosti&nbsp; njihove&nbsp; primene&nbsp; u&nbsp; preči&scaron;ćavanju&nbsp; otpadne&nbsp; vode&nbsp; u&nbsp; tercijarnom&nbsp; tretmanu&nbsp; na poluindustrijskim sistemima.<br />&nbsp;</p> / <p>The aim of this study was to investigate the decolorization efficiency of Reactive Red 120&nbsp; (RR120) synthetic solution using ferrioxalate (CuOFeB) and Al, Fe-bentonite (AlFeB) catalysts in&nbsp; Fenton&nbsp; and&nbsp; photo-Fenton&nbsp; process.&nbsp; So&nbsp; far,&nbsp; studies&nbsp; of the&nbsp; application&nbsp; of&nbsp; a&nbsp; solar-assisted&nbsp; heterogeneous Fenton process with various Fe loaded catalysts and with ferrioxalate complex have&nbsp; been published, but according to&nbsp;&nbsp; the author&rsquo;s knowledge, their comparison in terms of efficacy of&nbsp; decolorization&nbsp; has&nbsp; not&nbsp; been&nbsp; performed,&nbsp; which&nbsp; was&nbsp; one&nbsp; of&nbsp; the&nbsp; focus&nbsp; of&nbsp; research&nbsp; in&nbsp; this&nbsp; paper.&nbsp; In addition, the potential of solar energy represents&nbsp; 16.7% of the total utilized&nbsp; potential of renewable&nbsp; energy sources in Serbia, while the average solar radiation in&nbsp; Serbia is&nbsp; about 40% higher than the&nbsp; European average, making it very interesting for&nbsp; application in this type of treatment. In order to&nbsp; optimize the use of solar radiation and to improve&nbsp; the photocatalytic performance of the process, parabolic&nbsp; concentrating&nbsp; reactor&nbsp; was&nbsp; used&nbsp; for&nbsp; the&nbsp; first&nbsp; time.&nbsp; As&nbsp; a&nbsp; significant&nbsp; segment&nbsp; of&nbsp; the&nbsp; wastewater&nbsp; treatment&nbsp; technique&nbsp; during&nbsp; the&nbsp; degradation&nbsp; of&nbsp; persistent&nbsp; compounds,&nbsp; such&nbsp; as&nbsp; organic azo dye, solar photocatalysis was studied. Also, the potential of photolysis of hydrogen peroxide for&nbsp; decolorization of the synthetic dye solution was determined. Aim of the first phase of the study was synthesizing&nbsp; materials&nbsp; by&nbsp; using&nbsp; different&nbsp; methods&nbsp; of&nbsp; preparation,&nbsp; and&nbsp; construction&nbsp; of&nbsp; a&nbsp; solar&nbsp; parabolic reactor, which will be used in Fenton andphoto-Fenton dye degradation processes. The second phase involved the characterization of newlysynthesized materials and the optimization of the&nbsp; photocatalytic&nbsp; process&nbsp; by&nbsp; applying&nbsp; Fenton&nbsp; and&nbsp; photo-Fonton&nbsp; processes,&nbsp; as&nbsp; well&nbsp; as&nbsp; the&nbsp; determination&nbsp; of&nbsp; achieved efficiency&nbsp; of&nbsp; the&nbsp; appliedprocesses.&nbsp; Also, the degree&nbsp; of mineralization and the identification of degradation products after applied processes were determined. Application&nbsp; of the photo-Fenton process on a real effluent was conducted as well. Based on the obtained results&nbsp; during&nbsp; Fenton&nbsp; process&nbsp; and&nbsp; using&nbsp; both&nbsp; types&nbsp; of&nbsp; catalysts&nbsp; in&nbsp; periods&nbsp; of&nbsp; low&nbsp; and&nbsp; high&nbsp; intensity&nbsp; of&nbsp; radiation, from the aspect of achieving high efficiency of decolorization and smallest iron leaching,&nbsp; it&nbsp; can&nbsp; be&nbsp; concluded&nbsp; that&nbsp; the&nbsp; Fenton&nbsp; process&nbsp; is&nbsp; most effective&nbsp; at&nbsp; pH&nbsp; 3.&nbsp; AlFeB&nbsp; showed&nbsp; greater&nbsp; reactivity even at less used doses of 0.05&nbsp; g, compared to CuOFeB (0.2 g), and the possibility of using&nbsp; less&nbsp; hydrogen&nbsp; peroxide&nbsp; (2.5&nbsp; mM),&nbsp; achieving&nbsp; high&nbsp; efficiency&nbsp; and&nbsp; a&nbsp; high&nbsp; degree&nbsp; of mineralization. Higher intensity of solar radiationallows the reaction to be carried out at higher pH values when using both catalysts during the photo-Fenton process. This is particularly pronounced largest part in the decolorization process using the CuOFeB catalyst has&nbsp; a photolysis of hydrogen peroxide&nbsp; (80%).&nbsp; Contrary&nbsp; to&nbsp; these&nbsp; results,&nbsp; under&nbsp; the&nbsp; same&nbsp; reaction&nbsp; conditions,&nbsp; a&nbsp; higher&nbsp; doses&nbsp; of AlFeB catalyst (0.1 g) is needed at lower pH value&nbsp; of the reaction, and the process efficiency is significantly dependent on the initial concentration of H ₂O₂. The fact that in the preparation of the catalysts bentonite as a natural, abundant, inexpensive material was used and solar&nbsp; radiation as a renewable and alternative source of photons, the above results should&nbsp; be taken into account in the cost-effectiveness&nbsp; analysis&nbsp; of&nbsp; the&nbsp; applied&nbsp; process. Also,&nbsp; the&nbsp; application&nbsp; of&nbsp; advanced&nbsp; oxidation processes is considered as a proposal&nbsp; for the best available technique when it comes to the treatment of&nbsp; wastewater&nbsp; from&nbsp; the&nbsp; textile&nbsp; industry,&nbsp; while&nbsp; as&nbsp; additional&nbsp; new&nbsp; techniques,&nbsp; photooxidation&nbsp; is considered as a candidate and the possibility of their application in the treatment of wastewater in tertiary treatment on semi-industrial systems.</p>

Cette thèse est consacrée à l'étude des équations et systèmes de réaction-diffusion dans des milieux hétérogènes. Elle est divisée en deux parties. La première est dédiée à l'étude des équations de réaction-diffusion dans des milieux périodiques. Nous nous intéressons en particulier aux équations posées dans des domaines qui ne sont pas l'espace entier $\mathbb{R}^{N}$, mais des domaines périodiques, avec des "obstacles". Dans un premier chapitre, nous étudions l'effet de la géométrie du domaine sur la vitesse d'invasion des solutions. Après avoir dérivé une formule de type Freidlin-Gartner, nous construisons des domaines où la vitesse d'invasion est strictement inférieure à la vitesse critique des fronts. Nous donnons également des critères géométriques qui garantissent l'existence de directions où l'invasion se produit à la vitesse critique. Dans le chapitre suivant, nous donnons des conditions nécessaires et suffisantes pour garantir que l'invasion ait lieu, après quoi nous construisons des domaines où des phénomènes intermédiaires (blocage, invasion orientée) se produisent. La deuxième partie de cette thèse est consacrée à l'étude de modèles décrivant l'influence de lignes à diffusion rapide (une route, par exemple) sur la propagation d'espèces invasives. Il a en effet été observé que certaines espèces, dont le moustique-tigre, envahissent plus rapidement que prévu certaines zones proches du réseau routier. Nous étudions deux modèles : le premier décrit l'influence d'une route courbe sur la propagation. Nous nous intéressons en particulier au cas de deux routes non-parallèles. Le second modèle décrit l'influence d'une route sur une niche écologique, en présence d'un changement climatique. Le résultat principal est que l'effet de la route est ambivalent : si la niche est stationnaire, alors l'effet de la route est délétère. Cependant, si la niche se déplace, suite à un changement climatique, nous montrons que la route peut permettre à une population de survivre. Pour étudier ce second modèle, nous développons une notion de valeur propre principale généralisée pour des systèmes de type KPP, et nous dérivons une inégalité de Harnack, qui est nouvelle pour ce type de systèmes. / This thesis is dedicated to the study of reaction-diffusion equations and systems in heterogeneous media. It is divided into two parts. The first one is devoted to the study of reaction-diffusion equations in periodic media. We pay a particular attention to equations set on domains that are not the whole space $\mathbb{R}^{N}$, but periodic domains, with "obstacles". In a first chapter, we study how the geometry of the domain can influence the speed of invasion of solutions. After establishing a Freidlin-Gartner type formula, we construct domains where the speed of invasion is strictly less than the critical speed of fronts. We also give geometric criteria to ensure the existence of directions where the invasion occurs with the critical speed. In the second chapter, we give necessary and sufficient conditions to ensure that invasion occurs, and we construct domains where intermediate phenomena (blocking, oriented invasion) occur. The second part of this thesis is dedicated to the study of models describing the influence of lines with fast diffusion (a road, for instance) on the propagation of invasive species. Indeed, it was observed that some species, such as the tiger mosquito, invade faster than expected some areas along the road-network. We study two models : the first one describes the influence of a curved road on the propagation. We study in particular the case of two non-parallel roads. The second model describes the influence of a road on an ecological niche, in presence of climate change. The main result is that the effect of the road is ambivalent: if the niche is stationary, then effect of the road is deleterious. However, if the niche moves, because of a shifting climate, the road can actually help the population to persist. To study this model, we introduce a notion of generalized principal eigenvalue for KPP-type systems, and we derive a Harnack inequality, that is new for this type of systems.

In this paper, optimal control problems for semilinear parabolic equations with distributed and boundary controls are considered. Pointwise constraints on the control and on the state are given. Main emphasis is laid on the discussion of second order sufficient optimality conditions. Sufficiency for local optimality is verified under different assumptions imposed on the dimension of the domain and on the smoothness of the given data.

We consider a class of control problems governed by a linear parabolic initial-boundary value problem with linear-quadratic objective and pointwise constraints on the control. The control system contains different types of perturbations. They appear in the linear part of the objective functional, in the right hand side of the equation, in its boundary condition, and in the initial value. Making use of parabolic regularity in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm is improved to the supremum-norm.

The change in climate as a consequence of anthropogenic activities is a subject ofmajor concerns. In order to reduce the amount of greenhouse gas emissions inthe atmosphere, the utilization of renewable, fossil-free power generationapplications becomes inevitable. Geothermal and solar energy play a major rolein covering the increased demand for renewable energy sources of today’s andfuture’s society. A special focus hereby lies on the Concentrating Solar Powertechnologies and different geothermal concepts. The costs for producingelectricity through Concentrating Solar Power and therefore Parabolic Trough Collectorsas well as geothermal conversion technologies are still comparatively high. Inorder to minimize these expenses and maximize the cycle’s efficiency, thepossible synergies of a hybridization of these two technologies becomeapparent. This thesis therefore investigates the thermodynamic and economicbenefits and drawbacks of this combination from a global perspective. For that,a Parabolic Trough Collector system is combined with the geothermal conversionconcepts of Direct Steam, Single and Double Flash, Organic Rankine as well asKalina Cycles. The solar integrations under investigation are Superheat,Preheat and Superheat &amp; Reheat of the geothermal fluid. The thermodynamicanalysis focuses on the thermal and utilization efficiencies, as well as therequired Parabolic Trough Collector area. The results indicate that in the caseof the Superheat and Superheat &amp; Reheat setup, the thermal efficiency canbe improved for all geothermal concepts in comparison to their correspondinggeothermal stand-alone case. The Preheat cases, with the major contributionfrom solar energy, are not able to improve the cycle’s thermal efficiencyrelative to the reference setup. From an exergy perspective the findings varysignificantly depending on the applied boundary conditions. Still, almost allcases were able to improve the cycle’s performance compared to the referencecase. For the economic evaluation, the capital investment costs and thelevelized costs of electricity are studied. The capital costs increasesignificantly when adding solar energy to the geothermal cycle. The levelizedelectricity costs could not be lowered for any hybridization case compared tothe reference only-geothermal configurations. The prices vary between20.04 €/MWh and 373.42 €/MWh. When conducting a sensitivity analysison the solar system price and the annual mean irradiance, the Kalina Superheatand Superheat &amp; Reheat, as well as the Organic Rankine Preheathybridizations become cost competitive relative to the reference cases.Concluding, it is important to remark, that even if the hybridization of the ParabolicTrough and the different geothermal concepts makes sense from a thermodynamicperspective, the decisive levelized costs of electricity could not be improved.It is, however, possible that these costs can be further reduced under speciallocal conditions, making the addition of Parabolic Trough solar heat tospecific geothermal concepts favorable.

In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyper- bolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the second part, we consider hyperbolic conservation laws with stochas- tic forcing and study their approximations in the sense of Bhatnagar-Gross- Krook. In particular, we describe the conservation laws as a hydrodynamic limit of the stochastic BGK model as the microscopic scale vanishes. In the last part, we provide a new and fairly elementary proof of Skorkohod's classical theorem on existence of weak solutions to SDEs with continuous coefficients satisfying a suitable Lyapunov condition. 1

Many problems in continuum mechanics, especially in the theory of elastic materials, lead to nonlinear partial differential equations. The nonconvexity of their underlying energy potential is a challenge for mathematical analysis, since convexity plays an important role in the classical theories of existence and regularity. In the last years one main point of interest was to develop techniques to circumvent these difficulties. One approach was to use different notions of convexity like quasi-- or polyconvexity, but most of the work was done only for static (time independent) equations. In this thesis we want to make some contributions concerning existence, regularity and numerical approximation of nonconvex dynamical problems.

Many phenomena in our world can be described as differential equations in high dimensions. However, they are notoriously challenging to solve numerically due to the exponential growth in computational cost with increasing dimensions. This thesis explores an algorithm, known as deep BSDE, for solving high-dimensional partial differential equations and applies it to finance, namely European option pricing. In addition, an implementation of the method is provided that seemingly shortens the runtime by a factor of two, compared with the results in previous studies. From the results, we can conclude that the deep BSDE method does handle high-dimensional problems well. Lastly, the thesis gives the relevant prerequisites required to be able to digest the theory from an undergraduate level.

On s’intéresse à la dynamique dans un voisinage d’un point fixe d’une fonction antiholomorphe d’une variable. Dans un premier temps, on cherche à décrire et à comprendre l’espace des orbites dans un voisinage d’un point fixe multiple, appelé point parabolique, et à explorer les propriétés géométriques préservées par les changements de coordonnée. En particulier, on résout le problème de classification analytique des points paraboliques. Résoudre ce problème consiste à définir un module de classification complet qui permet de déterminer si deux germes de difféomorphismes antiholomorphes sont analytiquement conjugués dans un voisinage de leur point fixe parabolique. On examine également les applications du module à différents problèmes : i) extraction d’une racine n-ième antiholomorphe, ii) existence d’une courbe analytique invariante sous la dynamique d’un germe antiholomorphe parabolique et iii) centralisateur d’un germe antiholomorphe parabolique. Dans un second temps, on étudie les déploiements génériques d’un point fixe double, soit un point parabolique de codimension 1. Les questions sont de nature similaire, à savoir comprendre l’espace des orbites et les propriétés géométriques des déploiements. Afin de classifier les déploiements génériques, on déploie le module de classification pour les points paraboliques, ce qui permet d’obtenir des conditions nécessaires et suffisantes pour déterminer lorsque deux déploiements génériques sont équivalents. / We are interested in the dynamics in a neighbourhood of a fixed point of an antiholomorphic function of one variable. First, we want to describe and understand the space of orbits in a neighbourhood of a multiple fixed point, called a parabolic point, and to explore the geometric properties preserved by changes of coordinate. In particular, we solve the problem of analytical classification of parabolic fixed points. To solve this problem, we define a complete modulus of classification that allows to determine whether two germs of antiholomorphic diffeomorphisms are analytically conjugate in a neighbourhood of their parabolic fixed point. We also consider the applications of the modulus to different problems: i) extraction of an n-th antiholomorphic root, ii) existence of an invariant real analytical curve under the dynamics of a parabolic antiholomorphic germ, and iii) centraliser of a parabolic antiholomorphic germ. In the second part, we study generic unfoldings of a double fixed point, i.e. a parabolic point of codimension 1. The questions are similar in nature, namely to understand the space of orbits and the geometric properties of unfoldings. In order to classify generic unfoldings, the modulus of classification of the parabolic point is unfolded, thus providing the necessary and sufficient conditions to determine when two generic unfoldings are equivalent.