On an optimal domain with respect to (x,t) for a parabolic-type equation

Summary (translated from the Russian): "We give an existence theorem for an optimal couple Omega^{ast}, y^{ast} (x,t) that minimizes the functional J(Omega^{ast},y^{ast})=|y-y^{ast}; L_2(Omega)|^2, where Omega is a domain in {bf R}^2 and y=y(x,t) is a solution of the boundary value problem Ay=f(x,t) with a parabolic operator A."