Well posedness for a hyperbolic-parabolic Cauchy problem arising in population dynamics

Abstract

In some previous work [1]-[3], the authors have considered the diffusion of a population in a multilayered habitat, taking into account both the demographic structure, due to the age distribution of the individuals, and the spatial distribution related to population spread and diffusion. The development of the mathematical framework for this kind of problems leads the attention to a linear problem which incorporates all the features that make these kinds of problems unusual. This model is represented by a system of PDEs with discontinuous coefficients and data and sources at the boundaries between layers with different structure. In this paper we provide well posedness to such a problem together with regularity conditions, using $m$-accretiveness and fixed-points techniques.