Optimal Control in Models With Conductive‐radiative Heat Transfer

Abstract

In this paper an optimal control problem for the elliptic boundary value problem with nonlocal boundary conditions is considered. It is shown that the weak solutions of the boundary value problem depend smoothly on the control parameter and that the cost functional of the optimal control problem is Frechet differentiable with respect to the control parameter.

Temperature Modelling Within a Thin Material Sheet Involved in Conductive‐radiative Heat Transfer

“…If we adapt results from [1], [2], then we can get existence and uniform boundedness of solutions for the boundary value problem (2.1). As the form…”

“…The main reason is the fact that the sheet geometry is strongly degenerated in this situation. Thickness-width ratio for the sheet can achieve the value 1 15000 . In this paper we have analyzed the dependence of the weak solutions T δ of the boundary value problem (…”

Convergence of the Finite Volume Method for a Conductive-Radiative Heat Transfer Problem

“…The main interest of the paper is the applicability of the finite volume method to problems with nonlocal and nonlinear boundary conditions for a linear elliptic equation of the divergence type. As a rule, given class of boundary value problems arise in mathematical modeling of conductive-radiative heat transfer, see, for instance, [1,2,3,4,8,9].…”

“…For continuous case these difficulties are tackled via embedding theorems in Sobolev spaces, see, for instance [9], or specific trial functions, see, for instance [1,2,3], which unlikely have discrete analogues.…”