A reaction–diffusion system governed by nonsmooth semipermeability problem
A reaction–diffusion system governed by nonsmooth semipermeability problem
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DOI：
10.1080/00036811.2021.1921746
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发表时间：
2021-04
影响因子：
1.1
通讯作者：
Jinxia Cen;Guo-ji Tang;V. T. Nguyen;Shengda Zeng
中科院分区：
文献类型：
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作者：
Jinxia Cen;Guo-ji Tang;V. T. Nguyen;Shengda Zeng
近年来，在[唐国健，岑继新，阮文泰，等.微分变分-半变分不等式：存在性，唯一性，稳定性和收敛性. J Fixed Point Appl.2020; DOI：10.1007/s11784-020-00814-4]，研究了Banach空间中由非线性发展方程和含时变分-半变分不等式组成的一个综合系统-微分变分-半变分不等式（DVHVI，简称DVHVI）.我们证明了该解在温和意义下的存在性、唯一性和稳定性，以及DVHVI令人惊讶的收敛结果。然而，为了说明Tang等人的理论结果的适用性，本文研究了一个由非线性反应扩散方程描述的耦合动力系统，该方程由时间依赖的非光滑半渗透性问题描述。
Recently, in [Tang GJ, Cen JX, Nguyen VT, et al. Differential variational-hemivariational inequalities: existence, uniqueness, stability, and convergence. J Fixed Point Appl. 2020; DOI: 10.1007/s11784-020-00814-4],we studied a comprehensive system called differential variational-hemivar-iational inequality (DVHVI, for short) which is composed of a nonlinear evolution equation and a time-dependent variational-hemivariational inequality in Banach spaces. We have proved the existence, uniqueness, and stability of the solution in mild sense, as well as a surprising convergence result for DVHVI. However, to illustrate the applicability of those theoretical results in Tang et al., the present paper is devoted to explore a coupled dynamic system which is formulated by a nonlinear reaction–diffusion equation described by a time-dependent nonsmooth semipermeability problem.