Relaxation in population dynamics models with hysteresis

Sergey A. Timoshin; Toyohiko Aiki

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arXiv · 2004.12334

Relaxation in population dynamics models with hysteresis

Sergey A. Timoshin·Toyohiko Aiki

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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.

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Sergey A. Timoshin, Toyohiko Aiki. 2020-04-26. Relaxation in population dynamics models with hysteresis. https://arxiv.org/abs/2004.12334

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