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Existence and stability of bistable wavefronts in a nonlocal delayed reaction-diffusion epidemic system. (English) Zbl 1504.35115

Summary: In this paper, we consider the monotone travelling wave solutions of a reaction-diffusion epidemic system with nonlocal delays. We obtain the existence of monotone travelling wave solutions by applying abstract existence results. By transforming the nonlocal delayed system to a non-delayed system and choosing suitable small positive constants to define a pair of new upper and lower solutions, we use the contraction technique to prove the asymptotic stability (up to translation) of monotone travelling waves. Furthermore, the uniqueness and Lyapunov stability of monotone travelling wave solutions will be established with the help of the upper and lower solution method and the exponential asymptotic stability.

MSC:

35C07 Traveling wave solutions
35B51 Comparison principles in context of PDEs
35K57 Reaction-diffusion equations
35R09 Integro-partial differential equations
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