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On the existence of traveling waves for delayed reaction-diffusion equations. (English) Zbl 1167.35023
Summary: We study the existence of traveling wave solutions for reaction-diffusion equations with nonlocal delay, where reaction terms are not necessarily monotone. The existence of traveling wave solutions for reaction-diffusion equations with nonlocal delays is obtained by combining upper and lower solutions for associated integral equations and the Schauder fixed point theorem. The smoothness of upper and lower solutions is not required in this paper.

35K57Reaction-diffusion equations
34K30Functional-differential equations in abstract spaces
35R10Partial functional-differential equations
45K05Integro-partial differential equations
Full Text: DOI
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