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Zeitschrift für Analysis und ihre Anwendungen

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Volume 20, Issue 4, 2001, pp. 859–881
DOI: 10.4171/ZAA/1049

Published online: 2001-12-31

Free Boundary Problem for a One-Dimensional Transport Equation

Christina Kuttler[1]

(1) Universität Tübingen, Germany

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.

Keywords: Telegraph and transport equations, free boundary, correlated random walk

Kuttler Christina: Free Boundary Problem for a One-Dimensional Transport Equation. Z. Anal. Anwend. 20 (2001), 859-881. doi: 10.4171/ZAA/1049