Analysis of optimal boundary control for radiative heat transfer modeled by the $SP_{n}$-system
Pinnau, René
Commun. Math. Sci., Tome 5 (2007) no. 1, p. 951-969 / Harvested from Project Euclid
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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.
Publié le : 2007-12-15
Classification:  radiative heat transfer,  $SP_{n}$-approximation,  optimal boundary control,  first-order optimality system,  analysis,  adjoints,  35K55,  49K20,  80A20 
@article{1199377559,
     author = {Pinnau, Ren\'e},
     title = {Analysis of optimal boundary control for radiative heat transfer modeled by the $SP\_{n}$-system},
     journal = {Commun. Math. Sci.},
     volume = {5},
     number = {1},
     year = {2007},
     pages = { 951-969},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1199377559}
}

Pinnau, René. Analysis of optimal boundary control for radiative heat transfer modeled by the $SP_{n}$-system. Commun. Math. Sci., Tome 5 (2007) no. 1, pp.  951-969. http://gdmltest.u-ga.fr/item/1199377559/