A PDE model for the spatial dynamics of a voles population structured in age. (July 2020) - Coclite, G.M.; Donadello, C.; Nguyen, T.N.T.
Abstract: We prove existence and stability of entropy weak solutions for a macroscopic PDE model for the spatial dynamics of a population of voles structured in age. The model consists of a scalar PDE depending on time, t, age, a, and space x = ( x 1, x 2 ), supplemented with a non-local boundary condition at a = 0 . The flux is linear with constant coefficient in the age direction but contains a non-local term in the space directions. Also, the equation contains a term of second order in the space variables only. Existence of solutions is established by compensated compactness, see Panov (2009), and we prove stability by a doubling of variables type argument.