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Well-posedness and regularity for fractional damped wave equations

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Abstract

In this paper, we study the well-posedness and regularity of mild solutions for a class of time fractional damped wave equations, which the fractional derivatives in time are taken in the sense of Caputo type. A concept of mild solutions is introduced to prove the existence for the linear problem, as well as the regularity of the solution. We also establish a well-posed result for nonlinear problem. By applying finite dimensional approximation method, a compact result of solution operators is presented, following this, an existence criterion shows that the Lipschitz condition or smoothness of nonlinear force functions in some literatures can be removed. As an application, we discuss a case of time fractional telegraph equations.

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Acknowledgements

The authors are very grateful to the editor and reviewers for their valuable comments. Project supported by the Fundo para o Desenvolvimento das Ciências e da Tecnologia of Macau (Grant No. 0074/2019/A2) and National Natural Science Foundation of China (11671339) (12071396).

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Authors and Affiliations

  1. Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China

    Yong Zhou

  2. Faculty of Information Technology, Macau University of Science and Technology, Macau, 999078, China

    Yong Zhou

  3. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China

    Jia Wei He

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  1. Yong Zhou
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  2. Jia Wei He
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Correspondence to Yong Zhou.

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Communicated by Ansgar Jüngel.

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Zhou, Y., He, J.W. Well-posedness and regularity for fractional damped wave equations. Monatsh Math 194, 425–458 (2021). https://doi.org/10.1007/s00605-020-01476-7

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