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Homogenization limits and Wigner transforms
- P. Gérard, P. Markowich, N. Mauser, F. Poupaud
- Mathematics
- 1 April 1997
We present a theory for carrying out homogenization limits for quadratic functions (called “energy densities”) of solutions of initial value problems (IVPs) with anti-self-adjoint (spatial)…
ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
- A. Arnold, P. Markowich, G. Toscani, A. Unterreiter
- Mathematics
- 31 January 2001
It is well known that the analysis of the large-time asymptotics of Fokker-Planck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here…
Semiconductor equations
- P. Markowich, C. Ringhofer, C. Schmeiser
- Mathematics
- 1990
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
- W. Bao, Shi Jin, P. Markowich
- Mathematics, Physics
- 20 January 2002
In this paper we study time-splitting spectral approximations for the linear Schrodinger equation in the semiclassical regime, where the Planck constant e is small. In this regime, the equation…
The Stationary Semiconductor Device Equations.
- M. Sever, P. Markowich
- Mathematics
- 1 July 1987
1. Introduction.- 2. Mathematical Modeling of Semiconductor Devices.- 3. Analysis of the Basic Stationary Semiconductor Device Equations.- 4. Singular Perturbation Analysis of the Stationary…
Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
- W. Bao, D. Jaksch, P. Markowich
- Physics
- 13 March 2003
Entropy Dissipation Methods for Degenerate ParabolicProblems and Generalized Sobolev Inequalities
- J. Carrillo, A. Jüngel, P. Markowich, G. Toscani, A. Unterreiter
- Mathematics
- 1 May 2001
Abstract. We analyse the large-time asymptotics of quasilinear (possibly) degenerate parabolic systems in three cases: 1) scalar problems with confinement by a uniformly convex potential, 2)…
Global Solutions to the Coupled Chemotaxis-Fluid Equations
- Renjun Duan, A. Lorz, P. Markowich
- Mathematics
- 6 August 2010
In this paper, we are concerned with a model arising from biology, which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations through transport and external…
Kinetic Models for Chemotaxis and their Drift-Diffusion Limits
- F. A. Chalub, P. Markowich, B. Perthame, C. Schmeiser
- Mathematics
- 19 May 2004
Abstract.Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models…
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