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
The author(s) agree, that this abstract may be stored asfull text and distributed as such by abstracting services.