Analysis of control problems of nonmontone semilinear elliptic equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 80

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.

DOI : 10.1051/cocv/2020032
Classification : 35J61, 49J20, 49K20
Keywords: Optimal control, semilinear partial differential equation, optimality conditions 
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     author = {Casas, Eduardo and Mateos, Mariano and R\"osch, Arnd},
     title = {Analysis of control problems of nonmontone semilinear elliptic equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2020},
     publisher = {EDP Sciences},
     volume = {26},
     doi = {10.1051/cocv/2020032},
     mrnumber = {4162938},
     zbl = {1460.35150},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv/2020032/}
}
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Casas, Eduardo; Mateos, Mariano; Rösch, Arnd. Analysis of control problems of nonmontone semilinear elliptic equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 80. doi: 10.1051/cocv/2020032

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Cité par Sources :

The first two authors were partially supported by Spanish Ministerio de Economía y Competitividad under research project MTM2017-83185-P.