Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 262, Issue 9, Pages 4724-4770Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2016.12.017
Keywords
Three equations; Minimal wave speed; Persistence theory; LaSalle's invariance principle; Applications
Categories
Funding
- National Science Fund of China [11571284]
- Fundamental Research Funds for the Central Universities [XDJK2015C141]
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In this paper, we study the traveling wave solutions and minimal wave speed for a class of non-cooperative reaction diffusion systems consisting of three equations. Based on the eigenvalues, a pair of upper lower solutions connecting only the invasion-free equilibrium are constructed and the Schauder's fixed-point theorem is applied to show the existence of traveling semi-fronts for an auxiliary system. Then the existence of traveling semi-fronts of original system is obtained by limit arguments. The traveling semi-fronts are proved to connect another equilibrium if natural birth and death rates are not considered and to be persistent if these rates are incorporated. Then non-existence of bounded traveling semi-fronts is obtained by two-sided Laplace transform. Then the above results are applied to some disease-transmission models and a predator prey model. (C) 2016 Elsevier Inc. All rights reserved.
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