This paper discusses multiscale analysis for optimal control problems of linear parabolic equations with rapidly oscillating coefficients that depend on spatial and temporal variables. There are mainly three new results in the present paper. First, we obtain the convergence results with an explicit convergence rate for the multiscale asymptotic expansions of the solution of the optimal control problem in the case without constraints. Second, for a general bounded Lipschitz polygonal domain, the boundary layer solution is defined and the corresponding convergence results are also derived. Finally, an explicit convergence rate ε1/2in the presence of constraint is reported.
- Boundary layer solution
- Multiscale asymptotic expansion
- Optimal control
- Parabolic equation with rapidly oscillating coefficients
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics