Existence of solutions for -Laplacian equations.
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows
Existence of weak solutions for mixed problems of parabolic systems.
Existence of weak solutions for quasilinear elliptic equations involving the -Laplacian.
Existence results for the prescribed Scalar curvature on
This paper is devoted to the existence of conformal metrics on with prescribed scalar curvature. We extend well known existence criteria due to Bahri-Coron.
Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping
Explicit exponential decay bounds in quasilinear parabolic problems.
Explosion de solutions d'équations d'ondes quasi-linéaires en plusieurs dimensions d'espace
Explosion géométrique pour des systèmes quasi-linéaires
Explosion pour l’équation de Schrödinger au régime du “log log”
On présente dans cet exposé des résultats récents de Merle et Raphael sur l’analyse des solutions explosives de l’équation de Schrödinger critique. On s’intéresse en particulier à leur preuve du fait que les solutions d’énergie négative (dont on savait qu’elles explosaient par l’argument du viriel) et dont la norme est proche de celle de l’état fondamental, explosent au régime du “log log”et que ce comportement est stable.
Explosive solutions of semilinear elliptic systems with gradient term.
Estudiamos la existencia de soluciones del sistema elíptico no lineal Δu + |∇u| = p(|x|)f(v), Δv + |∇v| = q(|x|)g(u) en Ω que explotan en el borde. Aquí Ω es un dominio acotado de RN o el espacio total. Las nolinealidades f y g son funciones continuas positivas mientras que los potenciales p y q son funciones continuas que satisfacen apropiadas condiciones de crecimiento en el infinito. Demostramos que las soluciones explosivas en el borde dejan de existir si f y g son sublineales. Esto se tiene...
Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls.
Exponential attractors for semilinear wave equations with damping
Exponential convergence for a convexifying equation
We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573–1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.
Exponential convergence for a convexifying equation
We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573–1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.
Exponential convergence for a convexifying equation
We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573–1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.
Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics
We show that the entropy method, that has been used successfully in order to prove exponential convergence towards equilibrium with explicit constants in many contexts, among which reaction-diffusion systems coming out of reversible chemistry, can also be used when one considers a reaction-diffusion system corresponding to an irreversible mechanism of dissociation/recombination, for which no natural entropy is available.
Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics
We show that the entropy method, that has been used successfully in order to prove exponential convergence towards equilibrium with explicit constants in many contexts, among which reaction-diffusion systems coming out of reversible chemistry, can also be used when one considers a reaction-diffusion system corresponding to an irreversible mechanism of dissociation/recombination, for which no natural entropy is available.
Exponential decay for the semilinear wave equation with source terms.
Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping.