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2005-08

Propagation of graphs in two-dimensional inhomogeneous media

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


Series: 2005-08, Preprints

MSC:
35F25 Initial value problems for nonlinear first-order equations
35R05 Partial differential equations 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