Evolution problems involving state-dependent maximal monotone operators. Issue 1 (2nd January 2022) - Selamnia, Fatiha; Azzam-Laouir, Dalila; Monteiro Marques, Manuel D. P.
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.