Exact solutions for nonclassical Stefan problems.
Exemples d’instabilités pour des équations d’ondes non linéaires
Le but de l’exposé est de donner un guide de lecture pour un article de Gilles Lebeau où il est montré que le problème de Cauchy pour l’équation d’onde surcritique est mal posé au sens de Hadamard dans l’espace d’énergie, pour en dimension 3. La preuve repose sur des constructions d’optique géométrique et des analyses d’instabilité dans des régimes fortement non linéaires. On donnera les étapes de l’analyse en essayant de les situer dans leur contexte plus général : construction de solutions...
Existence and approximation results for gradient flows
This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space
Existence and attractivity results for a class of degenerate functional-parabolic problems
Existence and geometric properties of solutions of a free boundary problem in potential theory.
Existence and multiplicity of solutions for a differential inclusion problem involving the -Laplacian.
Existence and multiplicity of solutions to elliptic problems with discontinuities and free boundary conditions.
Existence and multiplicity results for degenerate elliptic equations with dependence on the gradient.
Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities
We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
Existence and nonexistence of global solutions of degenerate and singular parabolic systems.
Existence and nonexistence results for reaction-diffusion equations in product of cones
Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.
Existence and regularity for a minimum problem with free boundary.
Existence and regularity of local solutions to partial neutral functional-differential equations with infinite delay.
Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions.
Existence and uniqueness for one-phase Stefan problems of nonclassical heat equations with temperature boundary condition at a fixed face.
Existence and uniqueness of a classical solution of Fourier's first problem for nonlinear parabolic-elliptic systems.
Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data
Existence and uniqueness of solutions Cauchy problem for nonlinear infinite systems of parabolic differential-functional equations.
Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function
We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.
Existence and uniqueness of solutions of nonlinear infinite systems of parabolic differential-functional equations
We consider the Fourier first initial-boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations of parabolic type. The right-hand sides of the system are functionals of unknown functions. The existence and uniqueness of the solution are proved by the Banach fixed point theorem.