A reaction–diffusion system governed by nonsmooth semipermeability problem. Issue 18 (12th December 2022)

• Record Type: Journal Article
• Authors: Cen, Jinxia; Tang, Guo-ji; Nguyen, Van Thien; Zeng, Shengda
• Is Part Of: Applicable analysis. Volume 101:Issue 18(2022)
• Page Start: 6375
• Page End: 6387
• Publication Date: 2022-12-12
• Subjects: Reaction–diffusion equation -- nonsmooth semipermeability problem -- differential variational-hemivariational inequality -- C0-semigroup -- Clarke's subgradient; 35K55 -- 35K57 -- 47J20 -- 49J40 -- 58E35 -- 35K90 -- 46Txx; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1921746
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : 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.