![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
The purpose of this paper is to investigate a class of differential variational inequalities involving a constraint set in Banach spaces. A well-posedness result for the inequality is obtained, including the existence, uniqueness, and stability of the solution in mild sense. Further, we introduce a penalized problem without constraints and prove that the solution to the original inequality can be approached, as a parameter converges to zero, by the solution of the penalized problem. Finally, an application to a comprehensive obstacle parabolic-elliptic system delineates the abstract results.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
This project has received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement no. 823731 – CONMECH. It is also supported by the National Science Center of Poland under Maestro Project No. UMO-2012/06/A/ST1/00262, National Science Center of Poland under Preludium Project No. 2017/25/N/ST1/00611, NNSF of China [grant number 11671101], NSF of Guangxi [grant number 2018GXNSFDA138002], and International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland [grant number 3792/GGPJ/H2020/2017/0].