Traveling waves for non-local delayed diffusion equations via auxiliary equations |
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Authors: | Shiwang Ma |
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Institution: | School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China |
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Abstract: | In this paper, we study the existence of traveling wave solutions for a class of delayed non-local 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. |
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Keywords: | 34K30 35B40 35R10 58D25 |
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