Optimal design problems governed by the nonlocal p -Laplacian equation
In the present work, a nonlocal optimal design model has been considered as an approximation of the corresponding classical or local optimal design problem. The new model is driven by the nonlocal p-Laplacian equation, the design is the diffusion coefficient and the cost functional belongs to a broa...
| Autores: | ; ; |
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| Tipo de documento: | Artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Castilla-La Mancha |
| Repositorio: | RUIdeRA. Repositorio Institucional de la UCLM |
| OAI Identifier: | oai:ruidera.uclm.es:10578/28964 |
| Acceso en línea: | http://hdl.handle.net/10578/28964 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Approximation of partial differential equations Optimal Control Nonlocal elliptic equations G-Convergence p-Laplacian |
| _version_ | 1878736489103228928 |
|---|---|
| author | Andrés Abellán, María Fuensanta |
| author2 | Muñoz Martín, Julio Rosado Linares, Jesús |
| author2_role | author author |
| author_browse | Andrés Abellán, María Fuensanta Muñoz Martín, Julio Rosado Linares, Jesús |
| author_facet | Andrés Abellán, María Fuensanta Muñoz Martín, Julio Rosado Linares, Jesús |
| author_role | author |
| collection | RUIdeRA. Repositorio Institucional de la UCLM |
| description | In the present work, a nonlocal optimal design model has been considered as an approximation of the corresponding classical or local optimal design problem. The new model is driven by the nonlocal p-Laplacian equation, the design is the diffusion coefficient and the cost functional belongs to a broad class of nonlocal functional integrals. The purpose of this paper is to prove the existence of an optimal design for the new model. This work is complemented by showing that the limit of the nonlocal p-Laplacian state equation converges towards the corresponding local problem. Also, as in the paper by F. Andrés and J. Muñoz [J. Math. Anal. Appl. 429:288– 310], the convergence of the nonlocal optimal design problem toward the local version is studied. This task is successfully performed in two different cases: when the cost to minimize is the compliance functional, and when an additional nonlocal constraint on the design is assumed. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_8fdde71c4f5a818aacc939cfae7fe6b7 |
| institution | Universidad de Castilla-La Mancha |
| instname_str | Universidad de Castilla-La Mancha |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:ruidera.uclm.es:10578/28964 |
| publishDate | 2021 |
| publishDateSort | 2021 |
| publisher | AIMS |
| publisherStr | AIMS |
| reponame_str | RUIdeRA. Repositorio Institucional de la UCLM |
| spelling | Optimal design problems governed by the nonlocal p -Laplacian equation Andrés Abellán, María Fuensanta Muñoz Martín, Julio Rosado Linares, Jesús Approximation of partial differential equations Optimal Control Nonlocal elliptic equations G-Convergence p-Laplacian In the present work, a nonlocal optimal design model has been considered as an approximation of the corresponding classical or local optimal design problem. The new model is driven by the nonlocal p-Laplacian equation, the design is the diffusion coefficient and the cost functional belongs to a broad class of nonlocal functional integrals. The purpose of this paper is to prove the existence of an optimal design for the new model. This work is complemented by showing that the limit of the nonlocal p-Laplacian state equation converges towards the corresponding local problem. Also, as in the paper by F. Andrés and J. Muñoz [J. Math. Anal. Appl. 429:288– 310], the convergence of the nonlocal optimal design problem toward the local version is studied. This task is successfully performed in two different cases: when the cost to minimize is the compliance functional, and when an additional nonlocal constraint on the design is assumed. AIMS http://hdl.handle.net/10578/28964 |
| spellingShingle | Optimal design problems governed by the nonlocal p -Laplacian equation Andrés Abellán, María Fuensanta Approximation of partial differential equations Optimal Control Nonlocal elliptic equations G-Convergence p-Laplacian |
| title | Optimal design problems governed by the nonlocal p -Laplacian equation |
| title_full | Optimal design problems governed by the nonlocal p -Laplacian equation |
| title_fullStr | Optimal design problems governed by the nonlocal p -Laplacian equation |
| title_full_unstemmed | Optimal design problems governed by the nonlocal p -Laplacian equation |
| title_short | Optimal design problems governed by the nonlocal p -Laplacian equation |
| title_sort | Optimal design problems governed by the nonlocal p -Laplacian equation |
| topic | Approximation of partial differential equations Optimal Control Nonlocal elliptic equations G-Convergence p-Laplacian |
| topic_facet | Approximation of partial differential equations Optimal Control Nonlocal elliptic equations G-Convergence p-Laplacian |
| url | http://hdl.handle.net/10578/28964 |