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.
Authors
- dr Agnieszka Bartłomiejczyk link open in new tab ,
- Henryk Leszczyński,
- dr Milena Matusik
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.1016/j.jde.2022.09.018
- Category
- Publikacja w czasopiśmie
- Type
- artykuły w czasopismach
- Language
- angielski
- Publication year
- 2022
