numerical solutions of optimal control problems constrained by pdes with time-dependent coefficients

This paper develops a numerical approach to solve an optimal‎‎ control problem‎, ‎which is governed by a‎‎ parabolic partial differential equation (pde) with time-dependent coefficients‎. ‎first‎, ‎by‎ considering the pdes and using the hdmr method‎, ‎the‎‎ time-dependent coefficients are approximated and the pde is transformed into a set of pdes with constant coefficients‎.‎ in the next step‎, ‎these pde problems are transformed‎‎ to high-dimensional nonhomogeneous ordinary differential equation system (odes)‎. ‎then‎, ‎the homogeneous parts of these odes are solved using semigroup theory‎.‎ in the rest of the paper‎, ‎the original optimal‎‎ control problem is solved by utilizing the solution of the homogeneous‎‎ part.‎ ‎finally‎, ‎numerical results are presented.