Long-time behavior for a regularized scalar conservation law in the absence of genuine nonlinearity
Long-time behavior of nonlinear elastic waves
Longtime behavior of semilinear reaction-diffusion equations on the whole space
Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations
We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equation corresponding to initial values and source terms of sufficiently small size, as well as of small solutions to the corresponding stationary version, i.e. the quasilinear elliptic equation We then give conditions for the convergence, as , of the solution of the evolution equation to its stationary state.
Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system
We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids of the same density in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in the model. Moreover, diffusion of both components is taken into account. This leads to a coupled Navier-Stokes/Cahn-Hilliard system, which can describe the evolution of droplet formation and collision during the flow. We review some results on...
Long-time dynamics of an integro-differential equation describing the evolution of a spherical flame.
This article is devoted to the study of a flame ball model, derived by G. Joulin, which satisfies a singular integro-differential equation. We prove that, when radiative heat losses are too important, the flame always quenches; when heat losses are smaller, it stabilizes or quenches, depending on an energy input parameter. We also examine the asymptotics of the radius for these different regimes.
Long-Time Simulation of a Size-Structured Population Model with a Dynamical Resource
In this paper, we study the numerical approximation of a size-structured population model whose dependency on the environment is managed by the evolution of a vital resource. We show that this is a difficult task: some numerical methods are not suitable for a long-time integration. We analyze the reasons for the failure.
Long-time stability of noncharacteristic viscous boundary layers
We report our results on long-time stability of multi–dimensional noncharacteristic boundary layers of a class of hyperbolic–parabolic systems including the compressible Navier–Stokes equations with inflow [outflow] boundary conditions, under the assumption of strong spectral, or uniform Evans, stability. Evans stability has been verified for small-amplitude layers by Guès, Métivier, Williams, and Zumbrun. For large–amplitudes, it may be checked numerically, as done in one–dimensional case for isentropic...
Long-time vanishing properties of solutions of some semilinear parabolic equations
Loop groups and equations of KdV type
Loop spaces and Riemann-Hilbert problems
We present a survey of recent results concerned with generalizations of the classical Riemann-Hilbert transmission problem in the context of loop spaces. Specifically, we present a general formulation of a Riemann-Hilbert problem with values in an almost complex manifold and illustrate it by discussing two particular cases in more detail. First, using the generalized Birkhoff factorization theorem of A. Pressley and G. Segal we give a criterion of solvability for generalized Riemann-Hilbert problems...
L’opérateur de Casimir de
L'opérateur de temps-retard dans la théorie de la diffusion
Loss of exponential stability for a thermoelastic system with memory.
Lösung der Dirichletproblems und Konvergenz der Differenzenapproximation für elliptische Differentialgleichungen zweiter Ordnung.
Lösung des Dirichlet Problems bei Jordangebieten mit analytischem Rand durch Interpolation.
Lototsky-Schnabl Operators Associated with a Strictly Elliptic Differential Operator and Their Corresponding Feller Semigroup.
Louis Nirenberg and Klaus Schmitt: the joy of differential 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 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...