SIAM Journal on Control and Optimization, Volume 59, Issue 1, Page 693-708, January 2021.
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.

中文翻译：

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带有滞后的种群动力学模型中的松弛

SIAM控制与优化杂志，第59卷，第1期，第693-708页，2021
年1月。本论文涉及受状态依赖和非凸控制约束的非线性偏微分控制系统。该系统模拟了植被-捕食者-捕食者框架中种群的动态，并考虑了在此过程中出现的扩散和滞后效应。我们证明了系统解的存在，并表明它们在适当的意义上接近具有凸控制约束的系统解。