Rocky Mountain Journal of Mathematics

Existence and uniqueness of solutions for single-population

Agnieszka Bartłomiejczyk, Henryk Leszczyński, and Piotr Zwierkowski

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Abstract

We study a McKendrick-von Foerster type equation with renewal. This model is represented by a single equation which describes one species which produces young individuals. The renewal condition is linear but takes into account some history of the population. This model addresses nonlocal interactions between individuals structured by age. The vast majority of size-structured models are also treatable. Our model generalizes a number of earlier models with delays and integrals. The existence and uniqueness is proved through a fixed-point approach to an equivalent integral problem in $L^{\infty}\cap L^1$.

Article information

Source
Rocky Mountain J. Math., Volume 45, Number 2 (2015), 401-426.

Dates
First available in Project Euclid: 13 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1434208481

Digital Object Identifier
doi:10.1216/RMJ-2015-45-2-401

Mathematical Reviews number (MathSciNet)
MR3356622

Zentralblatt MATH identifier
1330.35463

Subjects
Primary: 35L45: Initial value problems for first-order hyperbolic systems 35L50: Initial-boundary value problems for first-order hyperbolic systems 35D05 92D25: Population dynamics (general)

Keywords
Existence uniqueness characteristics renewal

Citation

Bartłomiejczyk, Agnieszka; Leszczyński, Henryk; Zwierkowski, Piotr. Existence and uniqueness of solutions for single-population. Rocky Mountain J. Math. 45 (2015), no. 2, 401--426. doi:10.1216/RMJ-2015-45-2-401. https://projecteuclid.org/euclid.rmjm/1434208481


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