Dynamics of one- and two-dimensional kinks in bistable reaction-diffusion equations with quasidiscrete sources of reaction.
We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially inhomogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous works on homogeneous reaction terms, we derive asymptotically an equation governing the front motion, which is strongly nonlinear and, for the two-dimensional case, generalizes the classical mean curvature flow equation. We study the motion of one- and two-dimensional fronts, finding that the inhomogeneity acts as a "potential function" for the motion of the front; i.e., there is wave propagation failure and the steady state solution depends on the structure of the function describing the inhomogeneity. (c) 2001 American Institute of Physics.
Rotstein
Horacio G.
HG
Department of Chemistry and Volen Center for Complex Systems, Brandeis University, MS 015, Waltham, Massachusetts 02454-9110.
Zhabotinsky
Anatol M.
AM
Epstein
Irving R.
IR