05-08

Propagation of graphs in two-dimensional inhomogeneous media

by Deckelnick, K.; Elliott, C.M.

 

Preprint series: 05-08, Preprints

MSC:
35F25 Initial value problems for nonlinear first-order PDE, nonlinear evolution equations
35R05 PDE with discontinuous coefficients or data
65N15 Error bounds

 

Abstract: We consider the propagation of a front in a two-dimensional striated medium. In the case of a front that can be written as a graph over the real line we are led to an Eikonal equation for the height function which contains a possibly discontinuous coefficient. We prove existence and uniqueness of a viscosity solution in the sense of Ishii. Furthermore, we obtain an error bound for a monotone and consistent finite difference scheme. We conclude with some numerical tests.

Keywords: front propagation, Eikonal equation, viscosity solutions, striated medium, error bounds


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