Pinnau, René; Thömmes, Guido Optimal boundary control of glass cooling processes. (English) Zbl 1049.35044 Math. Methods Appl. Sci. 27, No. 11, 1261-1281 (2004). An optimal control problem for glass cooling processes is studied. The glass cooling is modelled using the \(SP_{1}\) approximations to the radiative heat transfer equations, in which the control variable is the temperature at the boundary of the domain. The resulting problem is a boundary control problem for a parabolic/elliptic system which is treated by a constrained optimization approach. Numerical methods for treating these control problems are investigated. Reviewer: Gheorghe Aniculăesei (Iaşi) Cited in 21 Documents MSC: 35B37 PDE in connection with control problems (MSC2000) 35K55 Nonlinear parabolic equations 49K20 Optimality conditions for problems involving partial differential equations 80A20 Heat and mass transfer, heat flow (MSC2010) 49N90 Applications of optimal control and differential games 49M05 Numerical methods based on necessary conditions 80M50 Optimization problems in thermodynamics and heat transfer Keywords:radiative heat transfer; glass manufacturing; thermal stresses; \(SP_N\) approximation; first-order optimality system; Lagrange multipliers; descent algorithm; parabolic/elliptic system PDFBibTeX XMLCite \textit{R. Pinnau} and \textit{G. Thömmes}, Math. Methods Appl. Sci. 27, No. 11, 1261--1281 (2004; Zbl 1049.35044) Full Text: DOI