A multiscale approach for optimal control problems of linear parabolic equations

Liqun Cao, Jianjun Liu, Walter Allegretto, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)3269-3291
Number of pages23
JournalSIAM Journal on Control and Optimization
Issue number6
Publication statusPublished - 31 Dec 2012


  • Boundary layer solution
  • Multiscale asymptotic expansion
  • Optimal control
  • Parabolic equation with rapidly oscillating coefficients

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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