Numerical solutions of optimal control problems constrained by PDEs with time-dependent coefficients

Document Type : Original Article

Author

Department of Mathematics, University of Qom, Qom, Iran.

Abstract

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 HDMR method, the
time-dependent coefficients  are approximated  and   the PDEs are transformed into several  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 homogeneous part. Finally, numerical results are presented.

Keywords

Main Subjects

Measure Algebras and Applications

Articles in Press, Accepted Manuscript
Available Online from 12 February 2026

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