Remarks on control and inverse problems for PDEs

This paper deals with recent results and open questions on the control and parameter identification of systems governed by PDEs. Among them, we find a few parabolic and hyperbolic equations, sometimes in the framework of a free-boundary problem. In the considered control problems, we try to govern t...

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Detalles Bibliográficos
Autor: Fernández Cara, Enrique
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/180942
Acceso en línea:https://hdl.handle.net/11441/180942
https://doi.org/10.1007/s40324-024-00363-7
Access Level:acceso abierto
Palabra clave:Control of PDEs
Inverse problems for PDEs
Theoretical and numerical analysis
Applications
Descripción
Sumario:This paper deals with recent results and open questions on the control and parameter identification of systems governed by PDEs. Among them, we find a few parabolic and hyperbolic equations, sometimes in the framework of a free-boundary problem. In the considered control problems, we try to govern the behavior of the solution(s) with a good (judicious) choice of the data. On the other hand, in the other (inverse) problems, the goal is to identify the value(s) of unknown data from particular observations of the solutions. We will recall a collection of optimal control, controllability and inverse problem assertions and will explain the arguments of proof. We will also present the results of some numerical experiments. Finally, we will state several open problems that can motivate future research on the subject.