Optimal control of semilinear parabolic equations with non-smooth pointwise-integral control constraints in time-space
This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form llu(t)ll L1(Ω) ≤ γ for t ∈ (0, T ). This limits the total control that can be applied to the system at any instant of time. The L1-norm of the constraint leads t...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2022 |
| País: | España |
| Recursos: | Universidad de Cantabria (UC) |
| Repositório: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.unican.es:10902/24444 |
| Acesso em linha: | http://hdl.handle.net/10902/24444 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Optimal control Semilinear parabolic equations Non-smooth control constraints First and second order optimality conditions |
| Resumo: | This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form llu(t)ll L1(Ω) ≤ γ for t ∈ (0, T ). This limits the total control that can be applied to the system at any instant of time. The L1-norm of the constraint leads to sparsity of the control in space, for the time instants when the constraint is active. Due to the non-smoothness of the constraint, the analysis of the control problem requires new techniques. Existence of a solution, first and second order optimality conditions, and regularity of the optimal control are proved. Further, stability of the optimal controls with respect to γ is investigated on the basis of different second order conditions. |
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