Relaxation in population dynamics models with hysteresis
Analysis of PDEs
2020-07-21 v2
Abstract
The present paper is concerned with a nonlinear partial differential control system subject to a state-dependent and nonconvex control constraint. This system models the dynamics of populations in the vegetation--prey--predator framework and takes account of diffusive and hysteresis effects appearing in the process. We prove the existence of solutions to our system and show that they are close in a suitable sense to solutions of the system with the convexified control constraint.
Cite
@article{arxiv.2004.12334,
title = {Relaxation in population dynamics models with hysteresis},
author = {Sergey A. Timoshin and Toyohiko Aiki},
journal= {arXiv preprint arXiv:2004.12334},
year = {2020}
}