Author(s) |
Ai, Shangbing
Du, Yihong
Jiao, Yujuan
Peng, Rui
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Publication Date |
2023-05
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Abstract |
<p>In this paper we establish a sharp existence result on weak traveling wave solutions for a general class of multi-species reaction–diffusion systems. Moreover, the minimal speed of the traveling waves is explicitly determined. Such a weak traveling wave solution connects the predator-free equilibrium point <i>E</i>0 at x = −∞ but needs not to connect the coexistence equilibrium <i>E</i><sup>∗</sup> at x = ∞. We apply this result to three important non-cooperative systems: the classical diffusive SIS system for the spread of infectious disease, a predator–prey system with age structure and a generalised Lotka–Volterra predator–prey system of one predator species feeding on <i>n</i> prey species, and prove with the aid of Lyapunov functions and the LaSalle invariance principle that their weak traveling wave solutions are actually traveling wave solutions that connect <i>E</i> <sup>∗</sup> at <i>x</i> = ∞. For the SIS system and the generalised Lotka–Volterra predator–prey system, we develop additional techniques to establish the boundedness of their weak traveling wave solutions before applying the LaSalle's invariance principle.</p>
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Citation |
Nonlinearity, 36(5), p. 2371-2402
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ISSN |
1361-6544
0951-7715
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Link | |
Publisher |
Institute of Physics Publishing Ltd
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Title |
Traveling wave solutions of a class of multi-species non-cooperative reaction–diffusion systems
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Type of document |
Journal Article
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Entity Type |
Publication
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