Latest News

About CAMQ

Information for Authors

Editorial Board

Browse CAMQ Online

Subscription and Pricing

CAMQ Contacts

CAMQ Home

 

Volume 7,     Number 1,     Spring 1999

 

A COMPETING REACTION-DIFFUSION SYSTEM
WITH SMALL CROSS-DIFFUSIONS
W.H. RUAN

Abstract. This paper is concerned 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 rates a1, a2 of species when the cross-diffusion coefficients are small. Our main goal is to determine the set Λ of ( a1, a2) so that the coupled system possesses positive steady-state solutions. It is shown that Λ is an unbounded, connected set in R+2 whose boundary consists of two monotone nondecreasing curves a1 = H1(a2) and a2 = H2(a1). For ( a1, a2 ) inside Λ, the system has positive solutions, and for (a1,a2) outside Λ, it has only the trivial and semi-trivial solutions.

 

Download PDF Files
 
(Subscribers Only)

© 2005, Canadian Applied Mathematics Quarterly (CAMQ)