Free boundary problem for a one-dimensional transport equation

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Abstract

For a linear transport equation in one space dimension with speeds in a compact interval and a general symmetric kernel for the change of velocity a problem with free boundary (Stefan problem) is stated. The case of constant speed corresponds to a Stefan problem for the damped wave equation (telegraph equation). Existence and uniqueness of the free boundary is shown, and the connection to the classical Stefan problem (parabolic limit) is exhibited.

Original languageEnglish
Pages (from-to)859-881
Number of pages23
JournalZeitschrift fur Analysis und ihre Anwendung
Volume20
Issue number4
StatePublished - 2001
Externally publishedYes

Keywords

  • Correlated random walk
  • Free boundary
  • Telegraph and transport equations

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