On attainability of optimal controls in coefficients for system of Hammerstein type with anisotropic p-Laplacian

Abstract

In this paper we consider an optimal control\ud problem (OCP) for the coupled system of a nonlinear monotone Dirichlet problem with anisotropic p-Laplacian and matrix-valued L^infinity(Omega, R^(NxN))-controls in its coefficients\ud and a nonlinear equation of Hammerstein type. Using the direct\ud method in calculus of variations, we prove the existence of an optimal control in considered problem and provide sensitivity analysis for a specific case of considered problem with respect to two-parameter regularization

Thermistor Problem: Multi-Dimensional Modelling, Optimization And Approximation

“…• the optimal control problem (4)-(6) is ill-posed and relations (1)-(3) require some relaxation (see, for instance, [Durante et al 2017, Kupenko andManzo 2016, Kupenko andManzo in press]).…”

On optimal <inline-formula><tex-math id="M1">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula>-control in coefficients for quasi-linear Dirichlet boundary value problems with <inline-formula><tex-math id="M2">\begin{document}$ BMO $\end{document}</tex-math></inline-formula>-anisotropic <inline-formula><tex-math id="M3">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian

“…We note that these assumptions on the class of matrices are essentially weaker than they usually are in the literature (see, for instance, [9,10,13,21,22]). In fact, we deal with a Dirichlet boundary value problem (BVP) for degenerate anisotropic elliptic equation with unbounded coefficients in its principal part and with L 1bounded control in the coefficient of the low-order term.…”