Shape stability of optimal control problems in coefficients for coupled system of Hammerstein type | Zendy

Olha P. Kupenko | Zendy; Rosanna Manzo | Zendy

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Shape stability of optimal control problems in coefficients for coupled system of Hammerstein type

Author(s) -

Olha P. Kupenko,

Rosanna Manzo

Publication year - 2015

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2015.20.2967

Subject(s) - mathematics , monotone polygon , nonlinear system , type (biology) , regular polygon , stability (learning theory) , omega , optimal control , dirichlet problem , class (philosophy) , perturbation (astronomy) , mathematical analysis , mathematical optimization , boundary value problem , geometry , computer science , ecology , physics , machine learning , artificial intelligence , biology , quantum mechanics

In this paper we consider an optimal control problem (OCP) for\udthe coupled system of a nonlinear monotone Dirichlet problem with matrixvalued\udL^Infinity(Ω;R^NxN)-controls in coefficients and a nonlinear equation of Hammerstein\udtype. Since problems of this type have no solutions in general, we\udmake a special assumption on the coefficients of the state equation and introduce\udthe class of so-called solenoidal admissible controls. Using the direct\udmethod in calculus of variations, we prove the existence of an optimal control.\udWe also study the stability of the optimal control problem with respect to the\uddomain perturbation. In particular, we derive the sufficient conditions of the\udMosco-stability for the given class of OCPs

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