期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 260, 期 3, 页码 2763-2791出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2015.10.017
关键词
Minimal wave speed; Traveling wave solution; Persistence theory; Negative one-sided Laplace transform; Applications
类别
资金
- National Science Fund of China [11171276, 11271369, 11201380]
- Fundamental Research Funds for the Central Universities [XDJK2015C141, SWU113048]
In this paper, we consider a class of non-cooperative diffusion reaction systems, which include prey predator models and disease-transmission models. The concept of weak traveling wave solutions is proposed. The necessary and sufficient conditions for the existence of such solutions are obtained by the Schauder's fixed-point theorem and persistence theory. The introduction of persistence theory is very technical and crucial. The LaSalle's invariance principle is applied to show that traveling wave solutions connect two equilibria. The nonexistence of traveling wave solutions is proved by introducing a negative one-sided Laplace transform. The results are applied to a prey predator model and a disease-transmission model with specific interaction functions. We find that the profile of traveling wave solutions may depend on different eigenvalues according to the corresponding condition, which is a new phenomenon. (C) 2015 Elsevier Inc. All rights reserved.
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