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Traveling waves for nonlocal delayed diffusion equations via auxiliary equations. (English) Zbl 1114.34061
Summary: We study the existence of traveling wave solutions for a class of delayed nonlocal reaction-diffusion equations without quasi-monotonicity. The approach is based on the construction of two associated auxiliary reaction-diffusion equations with quasi-monotonicity and a profile set in a suitable Banach space by using the traveling wavefronts of the auxiliary equations. Under monostable assumption, by using the Schauder’s fixed point theorem, we then show that there exists a constant \(c_{*} > 0\) such that for each \(c > c_{*}\), the equation under consideration admits a traveling wavefront solution with speed \(c\), which is not necessary to be monotonic.

MSC:
34K30 Functional-differential equations in abstract spaces
35B40 Asymptotic behavior of solutions to PDEs
35R10 Functional partial differential equations
34K10 Boundary value problems for functional-differential equations
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