Geodesic
A class of evolution differential inclusion systems
Izvestiya. Mathematics , Tome 88 (2024) no. 2, pp. 197-224

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The main purpose of this paper is to study an abstract system which consists of a non-linear differential inclusion with $C_0$-semigroups and history-dependent operators combined with an evolutionary non-linear inclusion involving pseudomonotone operators, which contains several interesting problems as special cases. We first introduce a hybrid iterative system by using the Rothe method, pseudomonotone operators theory, and a feedback iterative technique. Then, the existence and a priori estimates for solutions to a series of approximating discrete problems are established. Furthermore, through a limiting procedure for solutions of the hybrid iterative system, we show that the existence of solutions to the original problem.
Keywords: integro-differential inclusion systems, $C_0$-semigroup, Rothe method, feedback iterative technique.
Mots-clés : pseudomonotone 
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     author = {Jing Zhao and Zhenhai Liu and N. S. Papageorgiou},
     title = {A class of evolution differential inclusion systems},
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Jing Zhao; Zhenhai Liu; N. S. Papageorgiou. A class of evolution differential inclusion systems. Izvestiya. Mathematics , Tome 88 (2024) no. 2, pp. 197-224. http://geodesic.mathdoc.fr/item/IM2_2024_88_2_a1/