Analysis of optimal boundary control for radiative heat transfer modeled by the \(SP_1\)-system. (English) Zbl 1145.49015

Optimal boundary control problem modeling radiative heat transfer with quadratic cost performance index is considered. For that problem existence, uniqueness, regularity of bounded states and existence of optimal control are proved. The similar analysis for adjoint states is also performed. The system of the first order conditions of optimality is derived. The problem considered in the paper is of interests in many industrial high temperature processes and applications in which radiative heat transfer plays a dominant role, e.g., simulation of gas turbine combustion chambers, combustion in car engines. Because of high complexity of the real process, its approximation, the so-called diffusive-type \(SP_{1}\) system (see e.g. [M. Schäfer, M. Frank and R. Pinnau, Math. Models Methods Appl. Sci. 15, No. 4, 643–665 (2005; Zbl 1085.85002)]), is used.


49K20 Optimality conditions for problems involving partial differential equations
35B37 PDE in connection with control problems (MSC2000)
35K55 Nonlinear parabolic equations
80A20 Heat and mass transfer, heat flow (MSC2010)


Zbl 1085.85002
Full Text: DOI Euclid