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.
A PDE model for the spatial dynamics of a voles population structured in age / Coclite, G.; Donadello, C.; Nguyen, T. N. T.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 196:(2020), pp. 111805-111830. [10.1016/j.na.2020.111805]
A PDE model for the spatial dynamics of a voles population structured in age
Coclite, G.
;
2020-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
