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Classification of Initial Energy in a Pseudo-parabolic Equation with Variable Exponents and Singular Potential

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Abstract

This paper deals with a pseudo-parabolic equation with singular potential and variable exponents. First, we determine the existence and uniqueness of weak solutions in Sobolev spaces with variable exponents. Second, in the frame of variational methods, we classify the blow-up and the global existence of solutions completely using the initial energy. Third, we obtain lower and upper bounds of blow-up time for all possible initial energy. The results in this paper are compatible with the corresponding problems with constant exponents. Part results of the paper extend the recent ones in Lian et al. (J Differ Equ 269:4914–4959, 2020), Xu and Su (J Funct Anal 264:2732–2763, 2013), and Liu and Yu (J Funct Anal 274:1276–1283, 2018).

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Funding

This paper is supported by Shandong Provincial Natural Science Foundation of China (No. ZR2021MA003).

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Xizheng Sun & Zhiqing Han

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

    Bingchen Liu

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  1. Xizheng Sun
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  2. Zhiqing Han
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Correspondence to Zhiqing Han.

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Communicated by Vincenzo Ambrosio.

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Sun, X., Han, Z. & Liu, B. Classification of Initial Energy in a Pseudo-parabolic Equation with Variable Exponents and Singular Potential. Bull. Iran. Math. Soc. 50, 10 (2024). https://doi.org/10.1007/s41980-023-00844-x

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  • DOI: https://doi.org/10.1007/s41980-023-00844-x

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