1. Mixed semi-continuous perturbation of time -dependent maximal monotone operators and subdifferentials
- Author
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Castaing, Charles, Godet-Thobie, Christiane, Saïdi, Soumia, Monteiro Marques, Manuel, Université de Montpellier (UM), Laboratoire de Mathématiques de Bretagne Atlantique (LMBA), Université de Brest (UBO)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS), CNRS: UMR 6205, Laboratoire de mathématiques de Brest (LM), Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), LMPA, FSEI, Mohammed Seddik Ben Yahia University, Jijel-Algeria, and Universidade de Lisboa (ULISBOA)
- Subjects
pseudo-distance ,35B10 maximal monotone operator ,perturbation ,subdifferential operator ,34B15 ,[MATH]Mathematics [math] ,49J52 ,mixed semi-continuity ,Mathematics Subject Classification (2010). 34A60 ,evolution inclusion ,47H10 ,49J53 - Abstract
We are concerned in the present work with the existence of absolutely continuous solutions to a class of evolution problems governed by time-dependent maximal monotone operators A(t) of the form − du dt (t) ∈ A(t)u(t) + f (t, u(t)) + F (t, u(t)), where the perturbation is a sum of a mixed semi-continuous compact set-valued map F and a singlevalued map f. New variants dealing with a class of time-dependant subdifferential operators of the form − du dt (t) ∈ ∂ϕ(t, u(t)) + f (t, u(t)) + F (t, u(t)) are also investigated. Some applications are given.
- Published
- 2021