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.

最近，在 [Tang GJ, Cen JX, Nguyen VT, et al. 微分变分-半变分不等式：存在性、唯一性、稳定性和收敛性。J定点应用。2020；DOI: 10.1007/s11784-020-00814-4]，我们研究了一个综合系统，称为微分变分半变分不等式（简称DVHVI），它由非线性演化方程和时间相关的变分半变分不等式组成巴拿赫空间。我们从温和的意义上证明了解的存在性、唯一性和稳定性，以及 DVHVI 令人惊讶的收敛结果。然而，为了说明这些理论结果在 Tang 等人中的适用性，