| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 80 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2020032 | |
| Published online | 15 October 2020 | |
Analysis of control problems of nonmontone semilinear elliptic equations*
1
Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria,
39005
Santander, Spain.
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: mmateos@uniovi.es
Received:
13
June
2019
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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