Mellet, Antoine; Roquejoffre, Jean-Michel; Sire, Yannick Generalized fronts for one-dimensional reaction-diffusion equations. (English) Zbl 1180.35294 Discrete Contin. Dyn. Syst. 26, No. 1, 303-312 (2010). 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. Cited in 33 Documents 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 Keywords:fronts propagation; heterogeneous media; uniform nondegeneracy estimates PDFBibTeX XMLCite \textit{A. Mellet} et al., Discrete Contin. Dyn. Syst. 26, No. 1, 303--312 (2010; Zbl 1180.35294) Full Text: DOI