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A note on decay properties for the solutions of a class of partial differential equation with memory

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Abstract

The purpose of this article is to study decay properties for solutions of a class of PDEs with memory by Lyapunov functionals method. Moreover, we prove that when the kernels of the convolutions decay exponentially, the first and second order energy of the solutions decay exponentially. Also we show that when the kernels decay polynomially, these energies decay polynomially.

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Authors and Affiliations

  1. School of Mathematical Science and Computing Technology, Central South University, Changsha, 410075, Hunan, P.R. China

    Zai-yun Zhang, Xiu-jin Miao & Yue-zhong Chen

  2. Department of Mathematics, Hunan Institute of Science and Technology, Yueyang, 414006, Hunan, P.R. China

    Zai-yun Zhang

  3. School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, 530006, Guangxi, P.R. China

    Zhen-hai Liu

Authors
  1. Zai-yun Zhang
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  2. Zhen-hai Liu
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  3. Xiu-jin Miao
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  4. Yue-zhong Chen
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Correspondence to Zai-yun Zhang.

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Zhang, Zy., Liu, Zh., Miao, Xj. et al. A note on decay properties for the solutions of a class of partial differential equation with memory. J. Appl. Math. Comput. 37, 85–102 (2011). https://doi.org/10.1007/s12190-010-0422-7

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  • DOI: https://doi.org/10.1007/s12190-010-0422-7

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