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Abstract
We study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem in a semigroup setting. Since straight lines are more convenient in the exact and approximate solution of PDEs, we provide sufficient conditions of reducing more general equations. We give a difference scheme to find approximate solutions of the age-structured model. Finally, some numerical simulations are presented to demonstrate the convergence and stability of the difference scheme.
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Authors (3)
-
Henryk Leszczyński
- Uniweersytet Gdański
-
Milena Matusik dr
- Uniwersytet Gdański
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
JOURNAL OF DIFFERENTIAL EQUATIONS
no. 340,
pages 592 - 615,
ISSN: 0022-0396 - Language:
- English
- Publication year:
- 2022
- Bibliographic description:
- Bartłomiejczyk A., Leszczyński H., Matusik M.: Straightened characteristics of McKendrick-von Foerster equation// JOURNAL OF DIFFERENTIAL EQUATIONS -Vol. 340, (2022), s.592-615
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.jde.2022.09.018
- Sources of funding:
-
- Free publication
- Verified by:
- Gdańsk University of Technology
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