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Temporally Semidiscrete Approximation of a Dirichlet Boundary Control for a Fractional/Normal Evolution Equation with a Final Observation

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Abstract

Optimal Dirichlet boundary control for a fractional/normal evolution equation with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The convergence of a temporally semidiscrete approximation is rigorously established, where the control is not explicitly discretized and the state equation is discretized by a discontinuous Galerkin method in time. Numerical results are provided to verify the theoretical results.

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Authors and Affiliations

  1. School of Mathematics, Sichuan University, Chengdu, 610064, China

    Qin Zhou & Binjie Li

  2. China West Normal University, Nanchong, 637002, China

    Qin Zhou

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  1. Qin Zhou
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  2. Binjie Li
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Correspondence to Binjie Li.

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This work was supported in part by the National Natural Science Foundation of China under grant 11901410 and the Fundamental Research Funds for the Central Universities in China under grant 2020SCU12063.

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Zhou, Q., Li, B. Temporally Semidiscrete Approximation of a Dirichlet Boundary Control for a Fractional/Normal Evolution Equation with a Final Observation. J Sci Comput 88, 5 (2021). https://doi.org/10.1007/s10915-021-01522-y

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