Analysis of control problems of nonmontone semilinear elliptic equations
In this paper we study optimal control problems governed by a semilinear elliptic equation. The equation is nonmonotone due to the presence of a convection term, despite the monotonocity of the nonlinear term. The resulting operator is neither monotone nor coervive. However, by using conveniently a...
| Autores: | ; ; |
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| Tipo de documento: | Artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/20134 |
| Acceso en línea: | http://hdl.handle.net/10902/20134 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Optimal control Semilinear partial differential equation Optimality conditions |
| Sumario: | In this paper we study optimal control problems governed by a semilinear elliptic equation. The equation is nonmonotone due to the presence of a convection term, despite the monotonocity of the nonlinear term. The resulting operator is neither monotone nor coervive. However, by using conveniently a comparison principle we prove existence and uniqueness of solution for the state equation. In addition, we prove some regularity of the solution and differentiability of the relation control-to-state. This allows us to derive first and second order conditions for local optimality. |
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