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Heteroclinic connections for multidimensional bistable reaction-diffusion equations. (English) Zbl 1207.35028

Summary: Non-planar two-dimensional travelling fronts connecting an unstable one-dimensional periodic limiting state to a constant stable state are constructed for some reaction-diffusion equations with bistable nonlinearities. The minimal speeds are characterized in terms of the spatial period of the unstable limiting state. The limits of the minimal speeds and of the travelling fronts as the period converges to a critical minimal value or to infinity are analyzed. The fronts converge to flat fronts or to some curved fronts connecting an unstable ground state to a constant stable state.

MSC:

35B10 Periodic solutions to PDEs
35C07 Traveling wave solutions
35J61 Semilinear elliptic equations
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