Evolution problems involving state-dependent maximal monotone operators
2020; Taylor & Francis; Volume: 101; Issue: 1 Linguagem: Inglês
10.1080/00036811.2020.1738401
ISSN1563-504X
AutoresFatiha Selamnia, Dalila Azzam-Laouir, Manuel D. P. Monteiro Marques,
Tópico(s)Advanced Mathematical Modeling in Engineering
ResumoThe 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 −(du/dt)(t)∈A(t,u(t))u(t) where, for each (t,x)∈[0,T]×H, the maximal monotone operator A(t,x):H→2H 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.
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