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On the Controllability of a Class of Degenerate Parabolic Equations with Memory

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Abstract

In this paper, we study the null controllability and approximate controllability for a class of weakly degenerate parabolic equations with memory by means of boundary controls. Unlike the known result for the degenerate parabolic equation, the degenerate parabolic equation with memory in general is not null controllable. This is based on the observability inequality for the adjoint system, which does not hold in the corresponding space. On the other hand, we prove the approximate controllability property of it in a suitable state space with a boundary control, which acts on the degenerate boundary or the nondegenerate boundary.

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Acknowledgments

This work is partially supported by the NSF of China under grants 11371084, 11471070 and 11601213, the Training Program Project for Outstanding Young Teachers of Colleges and Universities in Guangdong Province under grant Yq2014116, and the Foundation for Young Talents in Higher Education of Guangdong under grant 2015KQNCX090.

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Authors and Affiliations

  1. School of Mathematics and Computation Science, Lingnan Normal University, Zhanjiang, 524048, China

    Xiuxiang Zhou

  2. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China

    Muming Zhang

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  1. Xiuxiang Zhou
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  2. Muming Zhang
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Correspondence to Muming Zhang.

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Zhou, X., Zhang, M. On the Controllability of a Class of Degenerate Parabolic Equations with Memory. J Dyn Control Syst 24, 577–591 (2018). https://doi.org/10.1007/s10883-017-9382-7

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  • DOI: https://doi.org/10.1007/s10883-017-9382-7

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