Analysis of control problems of nonmontone semilinear elliptic equations

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URI: http://hdl.handle.net/10902/20134
ISSN: 1292-8119
ISSN: 1262-3377
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Autoría
Casas Rentería, EduardoAutoridad Unican; Mateos Alberdi, MarianoAutoridad Unican; Rösch, Arnd
Fecha
2020-10-15
Derechos
© EDP Sciences; Société de Mathématiques Appliquées et Industrielles (SMAI). The original publication is available at www.esaim-cocv.org
Publicado en
ESAIM: Control, Optimisation and Calculus of Variations, 2020, 26, 80
Editorial
EDP Sciences
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Palabras clave
Optimal control
Semilinear partial differential equation
Optimality conditions
Resumen/Abstract
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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