Evolution problems involving state-dependent maximal monotone operators. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Selamnia, Fatiha; Azzam-Laouir, Dalila; Monteiro Marques, Manuel D. P.
• Is Part Of: Applicable analysis. Volume 101:Issue 1(2022)
• Page Start: 297
• Page End: 313
• Publication Date: 2022-01-02
• Subjects: B. Mordukhovich; Absolutely continuous variation -- maximal monotone operator -- pseudo-distance -- set-valued perturbation; 34H05 -- 34K35 -- 60H10 28A25 -- 28C20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1738401
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : The main objective of the present paper is to prove the existence of absolutely continuous solutions for an evolution problem in a Hilbert space H, of the form − ( d u / d t ) ( t ) ∈ A ( t, u ( t ) ) u ( t ) where, for each ( t, x ) ∈ [ 0, T ] × H, the maximal monotone operator A ( t, x ) : H → 2 H is of absolutely continuous variation in time and Lipschitz continuous in state, in the sense of the pseudo-distance introduced by A. A. Vladimirov. The perturbed problem is also considered.