Analysis of control problems of nonmontone semilinear elliptic equations

Autor:	Casas, Eduardo, Mateos, Mariano, Rösch, Arnd
Rok vydání:	2019
Předmět:	Mathematics - Optimization and Control Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
DOI:	10.1051/cocv/2020032
Popis:	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. Comment: 20 pages; In this version, we correct the end of Step 1 of the proof of Theorem 2.2 as well as some typos
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.13493 Zobrazit plný text záznamu View this record from Arxiv