Analysis of control problems of nonmontone semilinear elliptic equations
Optimization and Control
2020-06-11 v3 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1905.13493,
title = {Analysis of control problems of nonmontone semilinear elliptic equations},
author = {Eduardo Casas and Mariano Mateos and Arnd Rösch},
journal= {arXiv preprint arXiv:1905.13493},
year = {2020}
}
Comments
20 pages; In this version, we correct the end of Step 1 of the proof of Theorem 2.2 as well as some typos