| Abstract: |
| In this paper we investigate the global dynamics of an age-structured model with spatial structure including random diffusion and advection, and with a monotone nonlinearity in the birth rate. The existence, uniqueness and global stability of a positive equilibrium are given briefly via the theory of monotone dynamical systems. More interesting, we obtain the asymptotic behavior of principal eigenvalue and asymptotic profiles of the equilibrium under the large advection, small diffusion and large diffusion, respectively, which are new compared with the previous work on the diffusive age-structured models. Our tool is the principal spectral theory of linear age-structured operators with diffusion and advection. The proofs are based on the construction of new super-/sub-solutions to solve the issue of the nonlocal birth term which is specific in age-structured models. |
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