Dynamics for a diffusive epidemic model with a free boundary: sharp asymptotic profile
Abstract
This paper concerns the sharp asymptotic profiles of the solution of a diffusive epidemic model with one free boundary and one fixed boundary which is subject to the homogeneous Dirichlet boundary condition and Neumann boundary condition, respectively. The longtime behaviors has been proved to be governed by a spreading-vanishing dichotomy in LL, and when spreading happens, the spreading speed is determined in LLW. In this paper, by constructing some subtle upper and lower solutions, as well as employing some detailed analysis, we improve the results in LLW and obtain the sharp asymptotic spreading profiles, which show the homogeneous Dirichlet boundary condition and Neumann boundary condition imposed at the fixed boundary x=0 lead to the same asymptotic behaviors of h(t) and (u,v) near the spreading front h(t).
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