Equilibration rate for the linear inhomogeneous relaxation-time Boltzmann equation for charged particles

Maria J. Cáceres, José A. Carrillo, Thierry Goudon

    Research output: Contribution to journalArticleResearchpeer-review

    39 Citations (Scopus)

    Abstract

    We study the long-time behavior of a linear inhomogeneous Boltzmann equation. The collision operator is modeled by a simple relaxation towards the Maxwellian distribution with zero mean and fixed lattice temperature. Particles are moving under the action of an external potential that confines particles, i.e., there exists a unique stationary probability density. Convergence rate towards global equilibrium is explicitly measured based on the entropy dissipation method and apriori time independent estimates on the solutions. We are able to prove that this convergence is faster than any algebraic time function, but we cannot achieve exponential convergence.
    Original languageEnglish
    Pages (from-to)969-989
    JournalCommunications in Partial Differential Equations
    Volume28
    DOIs
    Publication statusPublished - 1 Jan 2003

    Keywords

    • Boltzmann equation
    • Entropy functional
    • Linear inhomogeneous equation

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