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Generalized fronts for one-dimensional reaction-diffusion equations. (English) Zbl 1180.35294

Summary: For a class of one-dimensional reaction-diffusion equations, we establish the existence of generalized fronts, as recently defined by Berestycki and Hamel. We also prove uniform nondegeneracy estimates, such as a lower bound on the time derivative on some level sets, as well as a lower bound on the spatial derivative.

MSC:

35K58 Semilinear parabolic equations
35K57 Reaction-diffusion equations
35K15 Initial value problems for second-order parabolic equations
35B45 A priori estimates in context of PDEs
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