Existence and approximation of nonlocal optimal design problems driven by parabolic equations
This work is a follow-up to a series of articles by the authors where the same topic for the elliptic case is analyzed. In this article, a class of nonlocal opti mal design problem driven by parabolic equations is examined. After a review of results concerning existence and uniqueness for the state...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Castilla-La Mancha |
| Repositorio: | RUIdeRA. Repositorio Institucional de la UCLM |
| OAI Identifier: | oai:ruidera.uclm.es:10578/28010 |
| Acceso en línea: | http://hdl.handle.net/10578/28010 |
| Access Level: | acceso abierto |
| Palabra clave: | Approximation of partial differential equations Integral equations Nonlocal parabolic equations Optimal control |
| Sumario: | This work is a follow-up to a series of articles by the authors where the same topic for the elliptic case is analyzed. In this article, a class of nonlocal opti mal design problem driven by parabolic equations is examined. After a review of results concerning existence and uniqueness for the state equation, a detailed formulation of the nonlocal optimal design is given. The state equation is of non local parabolic type, and the associated cost functional belongs to a broad class of nonlocal integrals. In the first part of the work, a general result on the existence of nonlocal optimal design is proved. The second part is devoted to analyzing the convergence of nonlocal optimal design problems toward the corresponding classical problem of optimal design. After a slight modification of the problem, either on the cost functional or by considering a new set of admissibility, the G-convergence for the state equation and, consequently, the convergence of the nonlocal optimal design problem are proved. |
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