Wavefronts for discrete two-dimensional nonlinear diffusion equations☆,☆☆

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Abstract

Existence of wavefronts for discrete two-dimensional evolution models involving diffusive terms with a nonlinear dependence on the discrete ‘gradients’ is studied. For small values of a control parameter, we prove existence of steady wavefronts. We investigate numerically the transition of steady fronts to traveling waves as the control parameter increases.

Keywords

Discrete wavefronts
Discrete nonlinear diffusion equations
Two dimensions
Dislocations

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This research was supported by Grant HB1997-0162 of the Spanish DGES.

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The author would like to thank J.R. Ockendon and S.J. Chapman for introducing her to the physics of dislocations.

Copyright © 2002 Published by Elsevier Ltd.