WebIn this paper, we consider optimal control problems associated with a class of quasilinear parabolic equations, where the coefficients of the elliptic part of the operator depend on the state function. We prove existence, uniqueness and regularity for the solution of the state equation. Then, we analyze the control problem. The goal is to get first and second order … WebThrough the use of the Maxwell theory, the semigroup theory, Helmholtz decomposition, and results on maximal monotone operators, we develop a mathematical theory including an …
A stochastic Galerkin method for Maxwell equations with
Weba semilinear parabolic equation with scalar control applied on the r.h.s. We ob-tain in particular an extension of Kelley’s condition, and the characterization of a quadratic growth property for a weak norm. Keywords parabolic equation, optimal control, singular arc, second order optimal-ity conditions, characterization of quadratic growth. 1 ... WebFor optimal control problems of the system coupled by Maxwell’s equations with nonlinear heat equation in microwave heating, there are several papers dealing with in recent years. Wei and Yin [7] discussed the existence and necessary conditions of the optimal control on the boundary electric field control. crystalline grain
Hyperbolic Maxwell Variational Inequalities for Bean
WebThis paper examines the mathematical and numerical analysis for optimal control problems governed by quasilinear H ( c u r l) -elliptic partial differential equations. We consider a … WebThe Maxwell equations are solved by a long-stencil fourth order finite difference method over a Yee grid, in which different physical variables are located at staggered mesh points. A careful treatment of the numerical values near the boundary is introduced, which in turn leads to a "symmetric image" formula at the "ghost" grid points. WebDec 12, 2024 · In this paper, we consider a distributed optimal control problem for the Cahn–Hilliard/Allen–Cahn equation with state-constraint. The objective is to force the coverage y to have some specified properties or achieve a certain goal. crystalline gold specimens