Positive Steady-State Solutions of a Competing Reaction-Diffusion System with Large Cross-Diffusion Coefficients

This paper deals with a coupled system of reaction-diffusion equations modeling the competition of two species with cross diffusion. We discuss the existence of positive steady-state solutions in relation to the intrinsic birth ratesa1,a2of species and the cross diffusion coefficients β12,β21. Our r...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 1996, Vol.197 (2), p.558-578
Main Author: Ruan, W.H.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
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Summary:This paper deals with a coupled system of reaction-diffusion equations modeling the competition of two species with cross diffusion. We discuss the existence of positive steady-state solutions in relation to the intrinsic birth ratesa1,a2of species and the cross diffusion coefficients β12,β21. Our results show that positive steady-state solutions exist ifa1anda2lie in certain range, or if β12and β21are sufficiently large.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1996.0039