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- Title
Multi-valued perturbation to evolution problems involving time dependent maximal monotone operators.
- Authors
Azzam-Laouir, Dalila; Belhoula, Warda; Castaing, Charles; Marques, M. D. P. Monteiro
- Abstract
In this paper, we study the existence of solutions for evolution problems of the form − du/dr(t) ∈ A(t)u(t) + F(t,u(t)) + f(t,u(t)), where, for each t, A(t) : D(A(t)) → 2H, is a maximal monotone operator in a Hilbert space H with continuous, Lipschitz or absolutely continuous variation in time. The perturbation ƒ is separately integrable on [0, T] and separately Lipschitz on H, while F is scalarly measurable and separately scalarly upper semicontinuous on H, with convex and weakly compact values. Several new applications are provided.
- Publication
Evolution Equations & Control Theory, 2020, Vol 9, Issue 1, p219
- ISSN
2163-2480
- Publication type
Academic Journal
- DOI
10.3934/eect.2020004