A PDE model for the spatial dynamics of a voles population structured in age. (July 2020)

• Record Type: Journal Article
• Authors: Coclite, G.M.; Donadello, C.; Nguyen, T.N.T.
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: 35Q92 -- 34B10; Population dynamics structured in age and space -- Parabolic–hyperbolic equation -- Non-local flux -- Boundary value problem -- Energy estimates -- Compensated compactness -- Doubling of variables; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111805
• Languages: English
• ISSNs: 0362-546X

Abstract

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.