Abstract In this paper we discuss the optimal control of a quasilinear parabolic state equation. Its form is leaned on kind problems arising for example when controlling anisotropic Allen–Cahn equation as model crystal growth. Motivated by application consider result gradient flow an energy functional. The term strongly monotone and obeys certain growth condition lower order non-monotone. discr...

This paper concerns with the state and proof existence uniqueness theorem of triple vector solution (TSVS) for nonlinear parabolic partial differential equations (TNPPDEs) ,and (TSVEs), under suitable assumptions. when continuous classical control (CCTCV) is given by using method Galerkin (MGA). The a optimal (CCTOCV) governing TNPPDEs conditions proved.

We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal controls and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the autho...

Abstract We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial of Sturm-Liouville type. first prove existence uniqueness solutions STFPEs on an open bounded interval their regularity. Then we show to a quadratic problem. derive adjoint problem using the right-Caputo derivative in tim...