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The Global ETD Search service is a free service for researchers
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Showing 51 to 54 of 54 (0.025 seconds)Spelling suggestions: "subject:"wellposedness"" "subject:"wellposeness""
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Étude de modèles de champ de phase de type Caginalp / Study of Caginalp type phase-field modelsDoumbé Bangola, Brice Landry 03 May 2013 (has links)
Ce rapport de thèse est consacré à l'étude de modèles de champ de phase de type Caginalp. Nous considérons ici, deux modèles : le premier étant une généralisation du modèle de champ de phase de Caginalp basée sur une généralisation de la loi de Maxwell-Cattaneo et le second une généralisation provenant de la théorie de la conduction de chaleur introduite par Chen et Gurtin. L'étude du premier modèle est faite aussi bien dans un domaine borné (avec un potentiel régulier puis dans le cas d'un potentiel non régulier), que dans un domaine non borné, en l'occurrence R3. Le second modèle est un problème de champ de phase avec un couplage (linéaire et non linéaire). Tout d'abord, l'existence, l'unicité et la régularité des solutions sont analysées aux moyens d'arguments classiques. Ensuite, l'existence d'ensembles bornés absorbants et compacts attractifs est établie, assurant ainsi l'existence de l'attracteur global. Enfin, dans certains cas, l'existence d'attracteurs exponentiels, ainsi que le comportement spatial des solutions lorsque le domaine spatial est un cylindre semi-infini tri-dimensionnel, sont analysés. / This thesis report is dedicated to the study of Caginalp type phase-field Models. Here, we consider two models: the first one being a generalization of the field phase Caginalp based on a generalization of the Maxwell-Cattaneo law and the second one coming from the theory of heat conduction involving two temperatures. We study the first model in bounded (with regular and irregular potentials) and unbounded (i.e. R3) domains. The second model is a phase-field one with coupling term (linear and nonlinear). Firstly, the existence, uniqueness and regularity of solutions are analyzed by means of classical arguments. Secondly, the existence of bounded absorbing sets and attractive compact is established. Such results ensures the existence of the global attractor. Finally, in some cases, the existence of exponential attractors, as well as the spatial behavior of solutions when the spatial domain is a three-dimensional semi-infinite cylinder, are analyzed.
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Étude asymptotique de modèles en transition de phase / Asymptotic study of phase transition modelsWehbe, Charbel 05 December 2014 (has links)
Ce rapport de thèse est consacré à l'étude de modèles de champ de phase de type Caginalp. Nous considérons ici, deux parties : la première étant une généralisation du modèle de champ de phase de Caginalp basée sur la loi de Maxwell-Cattaneo et la seconde traite le même modèle dans sa version conservative. L'étude dans les deux parties est faite dans un domaine borné. De plus, dans la première partie on distingue les cas de conditions aux bords de type Dirichlet ainsi que Neumann, tandis que dans la deuxième partie le modèle est étudié uniquement avec les conditions Dirichlet (avec un potentiel régulier puis un potentiel singulier). Tout d'abord, l'existence, l'unicité, et la régularité des solutions sont analysées aux moyens d'arguments classiques. Ensuite, l'existence d'ensembles bornés absorbants est établie. Enfin, dans certains cas, l'existence de l'attracteur global et d'attracteurs exponentiels sont analysés. / This thesis report is devoted to the study of Caginalp type phase-field Models. Here, we consider two parts : the first is a generalization of the Caginalp type phase-field model based on a generalization of the Maxwell-Cattaneo law and the second with the same model in its conservative version. The study in the two parts is made in a bounded domain. In addition, in the first part we distinguish cases of boundary conditions of Dirichlet and Neumann, while in the second part the model is studied only with Dirichlet conditions (with a regular potential and a singular potential). First, the existence, uniqueness, and regularity of solutions are analyzed by means of classical arguments. Then, the existence of bounded absorbing sets is established. Finally, in some cases, the existence of the global attractor and exponential attractors are analyzed.
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On some models in linear thermo-elasticity with rational material lawsMukhopadhyay, S., Picard, R., Trostorff, S., Waurick, M. 27 September 2019 (has links)
In the present work, we shall consider some common models in linear thermo-elasticity within a common structural framework. Due to the flexibility of the structural perspective we will obtain well-posedness results for a large class of generalized models allowing for more general material properties such as anisotropies, inhomogeneities, etc.
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Representation and Reconstruction of Linear, Time-Invariant NetworksWoodbury, Nathan Scott 01 April 2019 (has links)
Network reconstruction is the process of recovering a unique structured representation of some dynamic system using input-output data and some additional knowledge about the structure of the system. Many network reconstruction algorithms have been proposed in recent years, most dealing with the reconstruction of strictly proper networks (i.e., networks that require delays in all dynamics between measured variables). However, no reconstruction technique presently exists capable of recovering both the structure and dynamics of networks where links are proper (delays in dynamics are not required) and not necessarily strictly proper.The ultimate objective of this dissertation is to develop algorithms capable of reconstructing proper networks, and this objective will be addressed in three parts. The first part lays the foundation for the theory of mathematical representations of proper networks, including an exposition on when such networks are well-posed (i.e., physically realizable). The second part studies the notions of abstractions of a network, which are other networks that preserve certain properties of the original network but contain less structural information. As such, abstractions require less a priori information to reconstruct from data than the original network, which allows previously-unsolvable problems to become solvable. The third part addresses our original objective and presents reconstruction algorithms to recover proper networks in both the time domain and in the frequency domain.
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