Remarks on quenching.
Remarks on the asymptotical behaviour of solutions to some nonlinear parabolic equations
Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
We concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound from below the blow-up rate for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than , the expected one. Moreover, we state that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.
Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.
Remarks on the Klein-Gordon equation
Remarks on the large time behaviour of a nonlinear diffusion equation
Remarks on the qualitative behavior of the undamped Klein-Gordon equation
We present sufficient conditions on the initial data of an undamped Klein-Gordon equation in bounded domains with homogeneous Dirichlet boundary conditions to guarantee the blow up of weak solutions. Our methodology is extended to a class of evolution equations of second order in time. As an example, we consider a generalized Boussinesq equation. Our result is based on a careful analysis of a differential inequality. We compare our results with the ones in the literature.
Remarks on the wave equation with a nonlinear term with respect to the velocity
Remarks on weak stabilization of semilinear wave equations
If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble....
Remarks on weak stabilization of semilinear wave equations
If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble. ...
Remarque sur le problème de Cauchy pour une équation de Dirac non linéaire avec masse nulle
Remarques à propos du comportement, lorsque , des solutions des équations de Navier-Stokes associées à une force nulle
Remarques sur l'homogénéisation de certains problèmes quasi-linéaires
Representation theorem for stochastic differential equations in Hilbert spaces and its applications.
Representations of mild solutions of time-varying linear stochastic equations and the exponential stability of periodic systems.
Resolution of the time dependent Pn equations by a Godunov type scheme having the diffusion limit
We consider the Pn model to approximate the time dependent transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it has to give the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by Gosse to solve the P1 model...
Resonance functions of two-body Schrödinger operators
Resonant averaging for weakly nonlinear stochastic Schrödinger equations
Robin type conditions arising from concentrated potentials
Robust exponential attractors for singularly perturbed phase-field type equations.