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Analysis of control problems of nonmontone semilinear elliptic equations

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.

 Autoría: Casas E., Mateos M., Rösch A.,

 Fuente: ESAIM: Control, Optimisation and Calculus of Variations, 2020, 26, 80

Editorial: EDP Sciences

 Fecha de publicación: 15/10/2020

Nº de páginas: 21

Tipo de publicación: Artículo de Revista

 DOI: 10.1051/cocv/2020032

ISSN: 1292-8119,1262-3377

Proyecto español: MTM2017-83185-P

Url de la publicación: https://doi.org/10.1051/cocv/2020032