Fall 2024 APPROXIMATE CONTROLLABILITY FOR NONAUTONOMOUS INTEGRODIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY
Mamadou Abdoul Diop, Mohammed Elghandouri, Khalil Ezzinbi
J. Integral Equations Applications 36(3): 263-298 (Fall 2024). DOI: 10.1216/jie.2024.36.263

Abstract

We study the existence of mild solutions and the approximate controllability for nonautonomous integro-differential equations with state-dependent delay. We assume the approximate controllability of the linear part, and then we use resolvent operator theory to prove the approximate controllability of the nonlinear case. An example of the one-dimensional heat equation with memory is given to illustrate the basic idea our results.

Citation

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Mamadou Abdoul Diop. Mohammed Elghandouri. Khalil Ezzinbi. "APPROXIMATE CONTROLLABILITY FOR NONAUTONOMOUS INTEGRODIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY." J. Integral Equations Applications 36 (3) 263 - 298, Fall 2024. https://doi.org/10.1216/jie.2024.36.263

Information

Received: 19 December 2023; Revised: 2 April 2024; Accepted: 27 May 2024; Published: Fall 2024
First available in Project Euclid: 26 September 2024

Digital Object Identifier: 10.1216/jie.2024.36.263

Subjects:
Primary: 34K30 , 45K05 , 49J20 , 49J27 , 93B05

Keywords: approximate controllability , Integrodifferential equations , nonautonomous equations , Resolvent operators , state-dependent delay

Rights: Copyright © 2024 Rocky Mountain Mathematics Consortium

Vol.36 • No. 3 • Fall 2024
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