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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 1
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Articles

Evolution problems involving state-dependent maximal monotone operators

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Pages 297-313 | Received 09 Dec 2019, Accepted 01 Mar 2020, Published online: 11 Mar 2020
 

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 (du/dt)(t)A(t,u(t))u(t) where, for each (t,x)[0,T]×H, the maximal monotone operator A(t,x):H2H 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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Acknowledgments

The authors are very grateful to professor Charles Castaing for the interesting discussions and remarks related to this work, and a referee for the helpful remarks.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

M. D. P. M. M. was partially supported by Foundation for Science and Technology (FCT) [grant number UID/MAT/04561/2019].

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