Remarks on approximate harmonic maps.
Remarks on nonlinear biharmonic evolution equation of Kirchhoff type in noncylindrical domain.
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