Hamel, François; Roquejoffre, Jean-Michel Heteroclinic connections for multidimensional bistable reaction-diffusion equations. (English) Zbl 1207.35028 Discrete Contin. Dyn. Syst., Ser. S 4, No. 1, 101-123 (2011). 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. Cited in 15 Documents MSC: 35B10 Periodic solutions to PDEs 35C07 Traveling wave solutions 35J61 Semilinear elliptic equations Keywords:travelling fronts; reaction-diffusion equation; bistable nonlinearity; monostable connections; curved fronts PDFBibTeX XMLCite \textit{F. Hamel} and \textit{J.-M. Roquejoffre}, Discrete Contin. Dyn. Syst., Ser. S 4, No. 1, 101--123 (2011; Zbl 1207.35028) Full Text: DOI