On a second-order functional evolution problem with time and state dependent maximal monotone operators

Soumia Saïdi

doi:10.3934/eect.2021034

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2022, Volume 11, Issue 4: 1001-1035. Doi: 10.3934/eect.2021034

This issue Previous Article Next Article Approximate controllability of fractional neutral evolution systems of hyperbolic type

On a second-order functional evolution problem with time and state dependent maximal monotone operators

Soumia Saïdi

LMPA Laboratory, Department of Mathematics, Mohammed Seddik Ben Yahia University, Jijel-Algeria

Received: November 30, 2020

Revised: April 30, 2021

Early access: July 2021

Published: August 2022

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Abstract

The present paper proposes, in a real separable Hilbert space, to analyze the existence of solutions for a class of perturbed second-order state-dependent maximal monotone operators with a finite delay. The dependence of the operators is -in some sense- absolutely continuous (or bounded continuous) variation in time, and Lipschitz continuous in state. The approach to solve our problem is based on a discretization scheme. The uniqueness result is applied to optimal control.

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Mathematics Subject Classification: Primary: 34K09; Secondary: 49J52, 49J53.

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