Optimal boundary control of a hyperbolic system of heat equations (Q1930818)

The article refers to a mixed problem in a star domain for the hyperbolic system of heat equations, where the unknown functions are the temperature and the heat flux density. The model has been studied in a paper by \textit{R. K. Romanovskii} and \textit{O. G. Zhukova} [``Boundary control of heat transfer in a one-dimensional material. A hyperbolic model'' (English. Russian original), Differ. Equ. 43, No. 5, 667--672 (2007); translation from Differ. Uravn. 43, No. 5, 650--654 (2007)]. A boundary control problem is formulated. It is shown that boundary controls are elements of a set of functions satisfying some special conditions. One looks for the optimal control too.