Traveling wave solutions for reaction-diffusion systems

Publication: Research - peer-reviewJournal article – Annual report year: 2010

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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.
Original languageEnglish
JournalNonlinear Analysis: Theory, Methods & Applications
Publication date2010
Volume73
Journal number10
Pages3303-3313
ISSN0362-546X
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 2
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