Volume 26, 2020
|Number of page(s)||21|
|Published online||15 October 2020|
Analysis of control problems of nonmontone semilinear elliptic equations*
Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria,
2 Departamento de Matemáticas, Campus de Gijón, Universidad de Oviedo, 33203 Gijón, Spain.
3 Fakultät für Mathematik, Universtät Duisburg-Essen, 45127 Essen, Germany.
** Corresponding author: firstname.lastname@example.org
Accepted: 25 May 2020
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.
Mathematics Subject Classification: 35J61 / 49J20 / 49K20
Key words: Optimal control / semilinear partial differential equation / optimality conditions
© EDP Sciences, SMAI 2020
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