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Abstract
In the paper we provide systematic approaches to study existence and feedback control for a new evolutionary equation involving pseudomonotone operators. We first establish several existence results for the evolutionary equation by exploiting the Rothe method and using a surjectivity result for multivalued pseudomonotone operators. Then we show the existence of feasible pairs for the feedback control problem by assuming some sufficient conditions. Moreover, the existence of solutions to an evolutionary hemivariational inequality is presented.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data Availability Statements
All data generated or analyzed during this study are included in this published article (and its supplementary information files).
Additional information
Funding
The work is supported by the National Natural Science Foundation of China [grant number 12201137], the Special Fund for Science and Technological Bases and Talents of Guangxi [grant number GUIKE AD21220103] and the Start-up Project of Scientific Research on Introducing talents at school level in Guangxi Minzu University [grant number 2019KJQD04].