Laplace asymptotics for generalized K.P.P. equation
Least-energy solutions to a non-autonomous semilinear problem with small diffusion coefficient.
Local minimizers with vortex filaments for a Gross-Pitaevsky functional
This paper gives a rigorous derivation of a functional proposed by Aftalion and Rivière [Phys. Rev. A64 (2001) 043611] to characterize the energy of vortex filaments in a rotationally forced Bose-Einstein condensate. This functional is derived as a Γ-limit of scaled versions of the Gross-Pitaevsky functional for the wave function of such a condensate. In most situations, the vortex filament energy functional is either unbounded below or has only trivial minimizers, but we establish the existence...
Local stability of spike steady states in a simplified Gierer-Meinhardt system.
Locating the boundary peaks of least-energy solutions to a singularly perturbed Dirichlet problem
We consider the problemwhere is a smooth and bounded domain,
Long-time behavior for a regularized scalar conservation law in the absence of genuine nonlinearity
Low Mach number limit for viscous compressible flows
In this survey paper, we are concerned with the zero Mach number limit for compressible viscous flows. For the sake of (mathematical) simplicity, we restrict ourselves to the case of barotropic fluids and we assume that the flow evolves in the whole space or satisfies periodic boundary conditions. We focus on the case of ill-prepared data. Hence highly oscillating acoustic waves are likely to propagate through the fluid. We nevertheless state the convergence to the incompressible Navier-Stokes equations...
Low Mach number limit for viscous compressible flows
In this survey paper, we are concerned with the zero Mach number limit for compressible viscous flows. For the sake of (mathematical) simplicity, we restrict ourselves to the case of barotropic fluids and we assume that the flow evolves in the whole space or satisfies periodic boundary conditions. We focus on the case of ill-prepared data. Hence highly oscillating acoustic waves are likely to propagate through the fluid. We nevertheless state the convergence to the incompressible Navier-Stokes...
Metastability in the shadow system for Gierer-Meinhardt's equations.
Monotone finite difference domain decomposition algorithms and applications to nonlinear singularly perturbed reaction-diffusion problems.
Multiple boundary peak solutions for some singularly perturbed Neumann problems
Multiple clustered layer solutions for semilinear Neumann problems on a ball
Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains.
Multiplicity results for positive solutions to non-autonomous elliptic problems.
-widths for singularly perturbed problems
-widths for singularly perturbed problems
Kolmogorov -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
Navier–Stokes regularization of multidimensional Euler shocks
Nonlinear symmetric positive systems
Non-Stationary Burgers Flows with Vanishing Viscosity in Bounded Domains of IR3.
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical above which energy-minimizers have vortices, evaluations of the minimal energy as a function of , and the derivation of a limiting free-boundary problem.