Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A NEW APPROACH TO SOLVING OPTIMAL INNER CONTROL OF LINEAR PARABOLIC PDES PROBLEM

  • Mahmoudi, M. (Department of Mathematics, Ferdowsi University of Mashhad) ;
  • Kamyad, A.V. (Department of Mathematics, Ferdowsi University of Mashhad) ;
  • Effati, S. (Department of Mathematics, Ferdowsi University of Mashhad)
  • Received : 2011.02.12
  • Accepted : 2012.01.18
  • Published : 2012.09.30
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Abstract

In this paper, we develop a numerical method to solving an optimal control problem, which is governed by a parabolic partial differential equations(PDEs). Our approach is to approximate the PDE problem to initial value problem(IVP) in $\mathbb{R}$. Then, the homogeneous part of IVP is solved using semigroup theory. In the next step, the convergence of this approach is verified by properties of one-parameter semigroup theory. In the rest of paper, the original optimal control problem is solved by utilizing the solution of homogeneous part. Finally one numerical example is given.

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References

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