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.
Cite this article
Christina Kuttler, Free Boundary Problem for a One-Dimensional Transport Equation. Z. Anal. Anwend. 20 (2001), no. 4, pp. 859–881DOI 10.4171/ZAA/1049