Singular perturbations for a class of quasi-linear hyperbolic equations
Singularities in elliptic systems with absorption terms
Singularity patterns in a chemotaxis model.
Small analytic solutions to nonlinear weakly hyperbolic systems
Small time heat kernel behavior on Riemannian complexes.
Smoothness effect and decay on a class of non linear evolution equation
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise.
Solution semigroup and invariant manifolds for functional equations with infinite delay
It is proved that parabolic equations with infinite delay generate -semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations.
Solution to nonlinear gradient dependent systems with a balance law.
Solutions asymptotiques de l'équation de Dirac
Solutions en grand temps d'équations d'ondes non linéaires
Solutions for a hyperbolic system with boundary differential inclusion and nonlinear second-order boundary damping.
Solutions of an elliptic system with a nearly critical exponent
Solutions of Ginzburg-Landau equations and critical points of the renormalized energy
Solutions oscillantes des équations de Carleman
Solvability and asymptotics of solutions of crack-type boundary-contact problems of the ocuple-stress elasticity.
Some applications of parabolic comparison principles to the study of decay estimates.
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
We consider three types of semilinear second order PDEs on a cylindrical domain , where is a bounded domain in , . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of is reserved for time , the third type is an elliptic equation with a singled out unbounded variable . We discuss the asymptotic behavior, as , of solutions which are defined and bounded on .
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
Some decay properties for the damped wave equation on the torus
This article is a proceedings version of the ongoing work [1], and has been the object of a talk of the second author during the Journées “Équations aux Dérivées Partielles” (Biarritz, 2012).We address the decay rates of the energy of the damped wave equation when the damping coefficient does not satisfy the Geometric Control Condition (GCC). First, we give a link with the controllability of the associated Schrödinger equation. We prove that the observability of the Schrödinger group implies that...