Traveling wave solutions for reaction-diffusion systems |
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Authors: | Zhigui Lin Canrong Tian |
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Institution: | a School of Mathematical Science, Yangzhou University, Yangzhou 225002, Chinab Department of Mathematics, Technical University of Denmark, DK 2800, Kgs. Lyngby, Denmark |
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Abstract: | This paper is concerned with traveling waves of reaction-diffusion systems. The definition of coupled quasi-upper and quasi-lower solutions is introduced for systems with mixed quasimonotone functions, and the definition of ordered quasi-upper and quasi-lower solutions is also given for systems with quasimonotone nondecreasing functions. By the monotone iteration method, it is shown that if the system has a pair of coupled quasi-upper and quasi-lower solutions, then there exists at least a traveling wave solution. Moreover, if the system has a pair of ordered quasi-upper and quasi-lower solutions, then there exists at least a traveling wavefront. As an application we consider the delayed system of a mutualistic model. |
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Keywords: | primary 35K10 35K57 secondary 35R20 |
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