A PDE model for the spatial dynamics of a voles population structured in age

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=(x1,x2), supplemented with a non-local boundary condition at a=0. T...

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Bibliographic Details
Published inNonlinear analysis Vol. 196; p. 111805
Main Authors Coclite, G.M., Donadello, C., Nguyen, T.N.T.
Format Journal Article
LanguageEnglish
Published Elmsford Elsevier Ltd 01.07.2020
Elsevier BV
Subjects
Age
Boundary conditions
Boundary value problem
Compensated compactness
Doubling of variables
Energy estimates
Non-local flux
Parabolic–hyperbolic equation
Population dynamics structured in age and space
Doubling of variables
Parabolic–hyperbolic equation
Boundary value problem
Compensated compactness
Energy estimates
34B10
Population dynamics structured in age and space
Non-local flux
35Q92
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Summary: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=(x1,x2), 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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2020.111805