Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 171, Issue 2, Pages 294-314Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1006/jdeq.2000.3846
Keywords
fixed point theorem; traveling wavefront; delayed reaction-diffusion system; quasimonotonicity; supersolution; subsolution; predator-prey model; Belousov-Zhabotinskii reaction
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By using Schauder's fixed point theorem, we prove some existence results for traveling wavefronts of reaction-diffusion systems with quasimonotonicity reactions. More precisely. we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice. Finally. to illustrate our main results. wt: study the existence of traveling wavefronts are a delayed predator-prey model with diffusion as well as the reaction-diffusion system with the well-known Belousov Zhabotinskii reaction. and the obtained results improve the existing ones. (C) 2001 Academic Press.
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