Analysis of optimal boundary control for radiative heat transfer modeled by the $SP_{n}$-system

We present an analytic study of an optimal boundary control problem for the diffusive $SP_{1}$-system modeling radiative heat transfer. The cost functional is of tracking-type and the control problem is considered as a constrained optimization problem, where the constraint is given by the nonlinear parabolic/elliptic $SP_{1}$-system. We prove the existence, uniqueness and regularity of bounded states, which allows for the introduction of the reduced cost functional. Further, we show the existence of an optimal control, derive the first-order optimality system and analyze the adjoint system, for which we prove existence, uniqueness and regularity of adjoint states.

Keywords

radiative heat transfer, $SP_{n}$-approximation, optimal boundary control, first-order optimality system, analysis, adjoints

2010 Mathematics Subject Classification

35K55, 49K20, 80A20

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Published 1 January 2007