WorldCat Identities

Souplet, Philippe

Overview
Works: 36 works in 91 publications in 2 languages and 887 library holdings
Roles: Author, Thesis advisor, htt, Other, Opponent, Editor
Publication Timeline
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Most widely held works by Philippe Souplet
Superlinear parabolic problems : blow-up, global existence and steady states by P Quittner( )

37 editions published between 2000 and 2019 in English and held by 798 WorldCat member libraries worldwide

"This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology." "The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented." "The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics."--Jacket
Superlinear Parabolic Problems : Blow-up, Global Existence and Steady States by P Quittner( )

2 editions published in 2007 in English and held by 16 WorldCat member libraries worldwide

This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics
Etude qualitative des équations de Hamilton-Jacobi avec diffsuion non linéaire by Amal Attouchi( Book )

4 editions published in 2014 in English and held by 5 WorldCat member libraries worldwide

This thesis is devoted to the study of qualitative properties of solutions of an evolution equation of Hamilton-Jacobi type with a p-Laplacian diffusion. It is mainly concerned with the study of the effect of the non-linear diffusion on the gradient blow-up phenomenon. The main issues we are studying are: local existence and uniqueness, regularity, spatial profile of gradient blow-up and localization of the singularities. We provide examples where the gradient blow-up set is reduced to a single point. In Chapter 4, a viscosity solution approach is used to extend the blowing-up solutions beyond the singularities and an ergodic problem is also analyzed in order to study their long time behavior. In the penultimate chapter, we address the question of boundedness of global solutions to the one-dimensional problem. In the last chapter we prove a local in space, gradient estimate and we use it to obtain a Liouville-type theorem
Etude qualitative d'un système parabolique-elliptique de type Keller-Segel et de systèmes elliptiques non coopératifs by Alexandre Montaru( Book )

4 editions published in 2014 in English and held by 5 WorldCat member libraries worldwide

This thesis is concerned with the study of two problems : On the one hand, we consider a parabolic-elliptic system of Patlak-Keller-Segel type with a critical power type sensitivity. We study the radially symmetric solutions of this system on a ball of the euclidean space and obtain wellposedness and regularity results together with a blow-up alternative. As for the long time qualitative behaviour of the radial solutions, for any space dimension greater or equal to three, we show that a critical mass phenomenon occurs, which generalizes the wellknown case of dimension two but, with respect to the latter, with a very different qualitative behaviour in the case of the critical mass. When the mass is subcritical, we moreover show that the cell density converges uniformly with exponential speed toward the unique steady state. This result is valid for any space dimension greater or equal to two, which was, to our knowledge, not known even for the most studied case of dimension two. On the other hand, we study noncooperative (semilinear and fully nonlinear) elliptic systems. In the case of the whole space or of a half-space (or even for a cone), under a natural structure condition on the nonlinearities, we give sufficient conditions to have proportionnality of the components, which allows to reduce the system to a scalar equation and then to get classification and Liouville type results. In the case of a bounded domain, thanks to the obtained Liouville type theorems, the blow-up method of Gidas and Spruck then allows to get an a priori estimate on the bounded solutions and eventually to deduce the existence of a non trivial solution by a topological method using the degree theory
Propriétés globales de quelques équations d'évolution non linéaires du second ordre by Philippe Souplet( Book )

2 editions published in 1994 in French and held by 4 WorldCat member libraries worldwide

Cette thèse comporte trois parties indépendantes. La première est consacrée à l'étude des solutions globales d'équations non linéaires dissipatives de type hyperbolique. On s'intéresse tout d'abord au cas autonome, pour lequel on montre, par une méthode topologique originale, l'existence de solutions exceptionnelles, qui sont globales sur toute la droite réelle tout en étant non bornées. Nous donnons ensuite des résultats de stabilité pour l'équation d'évolution générale. Ceux-ci sont valables par exemple dans le cas de l'équation des ondes dans un domaine borné, où la dissipation est une puissance de la vélocité. On sait déjà que la différence de deux solutions décroît comme une constante que multiplie une puissance négative du temps. Nous établissons des estimations précises sur la constante, qui dépend des énergies initiales comme une puissance supérieure à 1. Dans le cas de l'équation différentielle ordinaire périodique, nous montrons que la stabilité est en fait exponentielle en temps et nous précisons également le comportement des constantes. Nous prouvons enfin l'optimalité des constantes obtenues, en utilisant l'existence de solutions globales sur toute la droite réelle. Dans la deuxième partie, nous étudions l'unicité des solutions antipériodiques pour des équations d'évolutions abstraites du second plan. Dans un premier temps, nous montrons qu'il y a unicité des solutions antipériodiques, lorsque la non-linéarité est assez petite. On donne différentes applications de ce résultat pour des systèmes différentiels et pour des équations d'ondes dans des domaines bornés, où nous explicitons des conditions suffisantes précises d'unicité. Nous montrons que ce résultat est spécifique au cadre antipériodique et qu'il ne peut pas s'étendre au cas général des solutions périodiques. Dans un deuxième temps, nous montrons que l'unicité des solutions antipériodiques n'est pas vraie en général sans hypothèse sur la taille de la non-linéarité. Nous construisons à cet effet des contre exemples très réguliers pour une équation des ondes et pour une équation différentielle ordinaire avec non-linéarité cubique, résolvant ainsi un problème ouvert depuis 1989. Dans la troisième partie, nous montrons d'abord le caractère non global des solutions pour une classe d'inégalités différentielles. En appliquant ensuite ce résultat et la méthode de convexité, nous obtenons l'explosion en temps fini des solutions de données initiales positives, pour des équations d'ondes où le terme de source est en compétition avec un terme de dissipation. Une autre application concerne une équation de la chaleur avec un terme de mémoire de type intégral. Les résultats sur l'équation des ondes sont complémentaires de ceux obtenus récemment par Georgiev et Todorova (1992), en utilisant la méthode d'énergie
Analyse qualitative des solutions de systèmes de réaction-diffusion et théorèmes de type Liouville by Quoc Hung Phan( )

2 editions published in 2013 in French and held by 4 WorldCat member libraries worldwide

This dissertation is devoted to the study of qualitative properties of solutions for some nonlinear elliptic and parabolic equations and systems. In the first part of the dissertation, we are interested in elliptic equations and systems with singular or degenerate coefficients of Hardy-Hénon type, in parabolic equations of the same type, and in a noncooperative parabolic system with constant coefficients. We obtain elliptic and parabolic Liouville-type theorems and we develop their applications : a priori estimates, singularity estimates in space or in time, decay estimates. In the second part, we prove the global existence and a priori bound of solutions of a Keller-Segel type, strongly coupled, parabolic system arising in crime modelling
Finite time blow up for a nonlinear heat equation by Philippe Souplet( Book )

2 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide

Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term by Philippe Souplet( Book )

2 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide

Poincaré's inequality and global solutions of a nonlinear parabolic equation by Philippe Souplet( Book )

2 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide

Estimations à priori et critères d'exploxion pour les problèmes paraboliques non-linéaires by Pierre Rouchon( Book )

2 editions published in 2002 in French and held by 3 WorldCat member libraries worldwide

Ce travail présente quelques résultats concernant les solutions de certaines équations paraboliques non-linéaires avec condition de Dirichlet au bord et donnée initiale positive. Il comporte deux parties distinctes. Dans la Partie I, nous travaillons dans des ouverts non bornés qui, typiquement, sont l'intérieur d'une surface de révolution. Nous considérons des équations dont les non-linéarités dépendent de puissances de la solution et de son gradient et donnons des résultats d'explosion en temps fini de la solution, suivant la décroissance à l'infini de la donnée initiale. Le critère obtenu dépend directement de la géométrie du domaine. Nous montrons que pour une large classe de domaines, ces résultats sont optimaux, i.e. il existe des solutions globales pour des données initiales ayant le même ordre de décroissance à l'infini. Nous généralisons les résultats d'explosion pour certains systèmes. Dans la Partie II, nous étudions les solutions globales positives d'équations comportant des termes de réaction non-locaux, dans des domaines bornés. Nous montrons qu'elles sont uniformément bornées : en d'autres termes, elles ne peuvent exploser en temps infini, ce qui n'est pas toujours le cas pour les termes de réaction locaux. Enfin, nous montrons l'existence de bornes universelles pour certaines de ces équations : après tout temps strictement positif, toutes les solutions globales et positives de ces équations sont bornées par une même constante indépendante de la donnée initiale. La démonstration repose en particulier sur de nouveaux effets régularisants pour ce type de problèmes
Self-similar subsolutions and blow-up for nonlinear parabolic equations by Philippe Souplet( Book )

2 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide

Analyse qualitative des solutions de systèmes de réaction-diffusion et théorèmes de type Liouville by Quoc Hung Phan( Book )

2 editions published in 2013 in French and held by 3 WorldCat member libraries worldwide

This dissertation is devoted to the study of qualitative properties of solutions for some nonlinear elliptic and parabolic equations and systems. In the first part of the dissertation, we are interested in elliptic equations and systems with singular or degenerate coefficients of Hardy-Hénon type, in parabolic equations of the same type, and in a noncooperative parabolic system with constant coefficients. We obtain elliptic and parabolic Liouville-type theorems and we develop their applications : a priori estimates, singularity estimates in space or in time, decay estimates. In the second part, we prove the global existence and a priori bound of solutions of a Keller-Segel type, strongly coupled, parabolic system arising in crime modelling
Méthode d'entropie et comportement asymptotique des solutions d'équations paraboliques linéaires et non-linéaires by Jean-Philippe Bartier( Book )

3 editions published between 2005 and 2019 in French and held by 3 WorldCat member libraries worldwide

Blow-up in nonlocal reaction-diffusion equations by Philippe Souplet( Book )

2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide

Les singularités en temps fini pour les équations semi-linéaires des ondes by Asma Azaiez( Book )

1 edition published in 2014 in English and held by 2 WorldCat member libraries worldwide

This thesis is devoted to the study of the finite time blow-up phenomena for the semilinear waves equations. We treat two models in this work. In the first part, we consider a complex-valued solution for the semilinear wave equation with power nonlinearity. We first characterize all the solutions of the associated stationary problem as a two-parameter family. Then, we use a dynamical system formulation to show that the solution in self-similar variables approaches some particular stationary one in the energy norm, in the non-characteristic case. This gives the blow-up profile for the original equation in the non-characteristic case.The second part is dedicated to the study of the semilinear wave equation with exponential nonlinearity in one space dimension. We generalize the results of Godin to a much larger class of initial data. We prove blow-up estimates near any point and give an optimal bound on the blow-up rate near the noncharacteristic points
A priori and universal estimates for global solutions of superlinear degenerate parabolic equations by Philippe Souplet( )

1 edition published in 2002 in English and held by 2 WorldCat member libraries worldwide

Optimal growth rates for a viscous Hamilton-Jacobi equation by Philippe Laurençot( )

1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide

An Example of Uniformly Recurrent Function which is not Almost Periodic by Alain Haraux( )

1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide

Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations] by Philippe Souplet( Book )

2 editions published in 1998 in English and held by 2 WorldCat member libraries worldwide

Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory by Philippe Souplet( )

1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide

 
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Superlinear parabolic problems : blow-up, global existence and steady states
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English (64)

French (11)