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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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