On stable solutions of quasilinear periodic-parabolic problems
On symmetric equilibrium of an isothermal gas with a free boundary and a body force.
On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations
In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last...
On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations
In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This...
On the behavior of solutions of parbolic equations with unbounded coefficients
On the collision of two solitons for the generalized KdV equation in the nonintegrable case
On the decay of the solutions of some nonlinear Schrödinger equations
On the Dirac delta as initial condition for nonlinear Schrödinger equations
On the existence of bounded solutions of nonlinear elliptic systems.
On the exponential growth of solutions to nonlinear hyperbolic equations.
On the instability of a class of periodic travelling wave solutions of the modified Boussinesq equation.
On the instability of ground states for a Davey-Stewartson system
On the instability of solitary-wave solutions for fifth-order water wave models.
On the -instability of fluid flows
On the local well-posedness of the KP equations
On the long time behavior of KdV type equations
In a series of recent papers, Martel and Merle solved the long-standing open problem on the existence of blow up solutions in the energy space for the critical generalized Korteweg- de Vries equation. Martel and Merle introduced new tools to study the nonlinear dynamics close to a solitary wave solution. The aim of the talk is to discuss the main ideas developed by Martel-Merle, together with a presentation of previously known closely related results.
On the long-time behaviour of compressible fluid flows subjected to highly oscillating external forces
We show that the global-in-time solutions to the compressible Navier-Stokes equations driven by highly oscillating external forces stabilize to globally defined (on the whole real line) solutions of the same system with the driving force given by the integral mean of oscillations. Several stability results will be obtained.
On the Principle of Linearized Stability for Varitional Inequalities.
On the role of the equal-area condition in internal layer stationary solutions to a class of reaction-diffusion systems.
On the stability of solitary waves for classical scalar fields