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: email@example.com
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.