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Pontryagin’s Maximum Principle for a Advection-Diffusion-Reaction Equation

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DOI: 10.4236/am.2012.312258    3,448 Downloads   5,393 Views  

ABSTRACT

In this paper we investigate optimal control problems governed by a advection-diffusion-reaction equation. We present a method for deriving conditions in the form of Pontryagin’s principle. The main tools used are the Ekeland’s variational principle combined with penalization and spike variation techniques.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Y. Xu, C. Xiao and H. Zhu, "Pontryagin’s Maximum Principle for a Advection-Diffusion-Reaction Equation," Applied Mathematics, Vol. 3 No. 12, 2012, pp. 1888-1891. doi: 10.4236/am.2012.312258.

References

[1] H. W. Lou and J. M. Yong, “Optimal Controls for Semilinear Elliptic Equations with Leaing Term Containing Controls,” SIAM Journal on Control and Optimization, Vol. 48, No. 4, 2009, pp. 2366-2387. doi:10.1137/080740301
[2] J. T. Oden and J. N. Reddy, “Variational Methods in Theoretical Mechanics,” Springer, Berlin and Heidelberg, 1983. doi:10.1007/978-3-642-68811-9
[3] L. Dede and A. Quarteroni, “Optimal Control and Numerical Adaptivity for Advection-Diffusion Equations,” Mathematical Modelling and Numerical Analysis, Vol. 39, No. 2, 2005, pp. 1019-1040.
[4] N. N. Yan and Z. J. Zhou, “A Priori and a Posteriori Error Analysis of Edge Stabilization Galerkin Method for the Optimal Control Problem Governed by Convection-Dominated Diffusion Equation,” Journal of Computational and Applied Mathematics, Vol. 223, No. 1, 2009, pp. 198-217. doi:10.1016/j.cam.2008.01.006
[5] R. Becker and B. Vexler, “Optimal Control of the Convection-Diffusion Equation Using Stabilized Finite Element Methods,” Numerische Mathematik, Vol. 106, No. 3, 2007, pp. 349-367. doi:10.1007/s00211-007-0067-0
[6] S. Micheletti and S. Perotto, “An Anisotropic Mesh Adaptation Procedure for an Optimal Control Problem of the Advection-Diffusion-Reaction Equation,” MOX-Report No. 15, 2008.
[7] S. S. Collis and M. Heinkenschloss, “Analysis of the Streamline Upwind/Petrov Galerkin Method Applied to the Solution of Optimal Control Problems,” Technical Report 02-01, Department of Computational and Applied Mathematics, Rice University, Houston, 2002.
[8] X. Li and J. Yong, “Optimal Control Theory for InfiniteDimensional Systems,” Birkh?user, Boston, 1995.

  
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