Existence and uniqueness of solutions for single-population McKendrick-von Foerster models with renewal

Agnieszka Bartłomiejczyk; Henryk Leszczyński; Piotr Zwierkowski

doi:10.1216/rmj-2015-45-2-401

Existence and uniqueness of solutions for single-population McKendrick-von Foerster models with renewal

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.

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Authors (3)

Agnieszka Bartłomiejczyk dr
Henryk Leszczyński
- Instytut Matematyki, UG Zakład Metod Numerycznych i Równań Różniczkowych
Piotr Zwierkowski
- Instytut Matematyki, UG Zakład Matematyki Stosowanej i Probabilistyki

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DOI:: Digital Object Identifier (open in new tab) 10.1216/RMJ-2015-45-2-401
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Keywords

EXISTENCE, UNIQUENESS, CHARACTERISTICS, RENEWAL

Details

Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS no. 45, edition 2, pages 401 - 426,
ISSN: 0035-7596
Language:: English
Publication year:: 2015
Bibliographic description:: Bartłomiejczyk A., Leszczyński H., Zwierkowski P.: Existence and uniqueness of solutions for single-population McKendrick-von Foerster models with renewal// ROCKY MOUNTAIN JOURNAL OF MATHEMATICS. -Vol. 45, iss. 2 (2015), s.401-426
DOI:: Digital Object Identifier (open in new tab) 10.1216/rmj-2015-45-2-401
Verified by:: Gdańsk University of Technology