On the Semigroups of Age-size Dependent Population Dynamics Wit}{ Spatial Diffusion
نویسندگان
چکیده
We are concerned with a population model with age-size dependence and spatial diffusion in the semigroup framework. We identify the infinitesimal generator and study its spectral properties. The dominant eigenvalue is thus determined. It is shown that the structure of the semigroup for the population with diffusion is essentially determined by those of the semigroups for the population without diffusion and the Laplacian. A logistic model with diffusion is also considered. A nonlinear semigroup is constructed to describe the evolution of the population. Existence and uniqueness of the global solution are proved and the large time behaviour is also investigated.
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