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Optimal Control for Fractional Diffusion Equations with Incomplete Data

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  • Gisèle Mophou

    (Université des Antilles et de la Guyane
    Université Ouaga 3S)

Abstract

We are concerned with the optimal control of time-fractional diffusion equations with missing boundary condition. Using the notion of no-regret control and least (or low) regret control developed by Lions, we first prove that the least regret control problem associated with the boundary fractional diffusion equation has a unique solution. Then we show that this solution converges to the no-regret control which we characterize by a singular optimality system.

Suggested Citation

  • Gisèle Mophou, 2017. "Optimal Control for Fractional Diffusion Equations with Incomplete Data," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 176-196, July.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-015-0817-6
    DOI: 10.1007/s10957-015-0817-6
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    References listed on IDEAS

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    1. Mophou, G. & Tao, S. & Joseph, C., 2015. "Initial value/boundary value problem for composite fractional relaxation equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 134-144.
    2. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
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