Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2000-02-23
Nonlinear Sciences
Pattern Formation and Solitons
Scientific paper
10.1063/1.1418459
We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially non-homogeneous. 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 non-homogeneity 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 non-homogeneity.
Epstein Irving R.
Rotstein Horacio G.
Zhabotinsky Anatol M.
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