Lyu Wenbin
School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China.
Math Biosci Eng. 2022 Sep 15;19(12):13458-13482. doi: 10.3934/mbe.2022629.
This paper establishes the existence of globally bounded classical solutions to a predator-prey model with attraction-repulsion taxis in a smooth bounded domain of any dimensions with Neumann boundary conditions. Moreover, the global stabilization of solutions with convergence rates to constant steady states is obtained. Using the local time integrability of the L-norm of solutions, we build up the basic energy estimates and derive the global boundedness of solutions by the Moser iteration. The global stability of constant steady states is established based on the Lyapunov functional method.
本文在任意维度的光滑有界区域中，针对具有吸引-排斥趋化性的捕食-食饵模型，在诺伊曼边界条件下建立了全局有界经典解的存在性。此外，还得到了解以收敛速率趋于常数稳态的全局稳定性。利用解的(L)-范数的局部时间可积性，我们建立了基本能量估计，并通过莫泽迭代推导了解的全局有界性。基于李雅普诺夫泛函方法建立了常数稳态的全局稳定性。
