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Archive for Rational Mechanics and Analysis

, Volume 195, Issue 1, pp 75–116 | Cite as

Stability of the Front under a Vlasov–Fokker–Planck Dynamics

  • R. EspositoEmail author
  • Y. Guo
  • R. Marra
Article

Abstract

We consider a kinetic model for a system of two species of particles interacting through a long range repulsive potential and a reservoir at given temperature. The model is described by a set of two coupled Vlasov–Fokker–Plank equations. The important front solution, which represents the phase boundary, is a stationary solution on the real line with given asymptotic values at infinity. We prove the asymptotic stability of the front for small symmetric perturbations.

Keywords

Boltzmann Equation Symmetry Property Energy Estimate Null Space Orthogonal Complement 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di L’AquilaCoppitoItaly
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA
  3. 3.Dipartimento di Fisica and Unita’ INFNUniversita’ di Roma Tor VergataRomaItaly

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