Nontrivial large-time behaviour in bistable reaction-diffusion equations
Bistable reaction-diffusion equations are known to admit one-dimensional travelling waves which are globally stable to one-dimensional perturbations. These planar waves are also stable to two-dimensional perturbations. These perturbations decay in the direction transverse to the wave, in an integrable fashion. The authors first prove that this result breaks down when the integrability condition is removed and exhibit a large-time dynamics similar to that of the heat equation. This result is then applied to the study of the large-time behaviour of conical-shaped fronts in the plane and cases where the dynamics is given by that of two advection-diffusion equations are investigated.
scientific article; zbMATH DE number 5610623
scientific article