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arXiv · 1905.13493

Analysis of control problems of nonmontone semilinear elliptic equations

Eduardo Casas·Mariano Mateos·Arnd Rösch
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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.

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Eduardo Casas, Mariano Mateos, Arnd Rösch. 2020-06-10. Analysis of control problems of nonmontone semilinear elliptic equations. https://doi.org/10.1051/cocv%2F2020032

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