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Research Article | Open Access

The well-posedness for semilinear time fractional wave equations on RN

Yong Zhou1,2, Jia Wei He3( ), Ahmed Alsaedi2, Bashir Ahmad2
Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
College of Mathematics and Information Science, Guangxi University, Nanning 530004, China
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Abstract

This paper is concerned with the semilinear time fractional wave equations on the whole Euclidean space, also known as the super-diffusive equations. Considering the initial data in the fractional Sobolev spaces, we prove the local/global well-posedness results of L2-solutions for linear and semilinear problems. The methods of this paper rely upon the relevant wave operators estimates, Sobolev embedding and fixed point arguments.

Keywords

fractional derivativefractional wave equationswell-posedness

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Electronic Research Archive
Volume 30 Issue 8,
August 2022
Pages 2981-3003
DOI: 10.3934/era.2022151

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Cite this article:
Zhou Y, He JW, Alsaedi A, et al. The well-posedness for semilinear time fractional wave equations on RN. Electronic Research Archive, 2022, 30(8): 2981-3003. https://doi.org/10.3934/era.2022151

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Received: 29 November 2021
Revised: 23 March 2022
Accepted: 26 May 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)