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...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Mateos Alberdi, Mariano, Rösch, Arnd
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/20134
Acceso en línea:http://hdl.handle.net/10902/20134
Access Level:acceso abierto
Palabra clave:Optimal control
Semilinear partial differential equation
Optimality conditions
Descripción
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.