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Classification of initial energy in a pseudo-parabolic equation with variable exponents

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Abstract

This paper deals with a pseudo-parabolic equation with variable exponents, subject to homogeneous boundary conditions with initial data in \(H_0^1(\varOmega )\). By using energy functional and Nehari functional, we classify blow-up and global existence of weak solutions in variable Sobolev spaces completely for subcritical, critical, and super critical initial energy, respectively.

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Acknowledgements

The authors would like to express their sincerely thanks to the Editor and the Reviewers for the helpful comments on this paper.

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Authors and Affiliations

  1. College of Science, China University of Petroleum, Qingdao, 266580, People’s Republic of China

    Fengjie Li, Jiaqi Liu & Bingchen Liu

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  1. Fengjie Li
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  2. Jiaqi Liu
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  3. Bingchen Liu
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Correspondence to Bingchen Liu.

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This paper is supported by Shandong Provincial Natural Science Foundation, China (No. ZR2020MA020).

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Li, F., Liu, J. & Liu, B. Classification of initial energy in a pseudo-parabolic equation with variable exponents. Anal.Math.Phys. 11, 148 (2021). https://doi.org/10.1007/s13324-021-00583-4

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