Hydrodynamic limits for kinetic equations and the diffusive approximation of radiative transport for acoustic waves

Manuel Portilheiro*, Athanasios E. Tzavaras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider a class of kinetic equations, equipped with a single conservation law, which generate L1-contractions. We discuss the hydrodynamic limit to a scalar conservation law and the diffusive limit to a (possibly) degenerate parabolic equation. The limits are obtained in the "dissipative" sense, equivalent to the notion of entropy solutions for conservation laws, which permits the use of the perturbed test function method and allows for simple proofs. A general compactness framework is obtained for the diffusive scaling in L1. The radiative transport equations, satisfied by the Wigner function for random acoustic waves, present such a kinetic model that is endowed with conservation of energy. The general theory is used to validate the diffusive approximation of the radiative transport equation.

Original languageEnglish (US)
Pages (from-to)529-565
Number of pages37
JournalTransactions of the American Mathematical Society
Volume359
Issue number2
DOIs
StatePublished - Feb 1 2007

Keywords

  • Diffusive limit
  • Radiative transport

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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