Abstract
In this paper, we study an initial boundary value problem for a $p$-Laplacian hyperbolic equation with logarithmic nonlinearity. By combining the modified potential well method with the Galerkin method, the existence of the global weak solution is studied, and the polynomial and exponential decay estimation under certain conditions are also given. Moreover, by using the concavity method and other techniques, we obtain the blow up results at finite time.
Funding Statement
The work is supported by the National Natural Science Foundation of China (No. 12171054) and the “Thirteen Five” Scientific and Technological Research Planning Project of the Department of Education of Jilin Province in China (JJKH20190547KJ, JJKH20200727KJ).
Acknowledgments
We are very grateful to the anonymous referees for their valuable suggestions that improved the article.
Citation
Ying Chu. Yuqi Wu. Libo Cheng. "Blow up and Decay for a Class of $p$-Laplacian Hyperbolic Equation with Logarithmic Nonlinearity." Taiwanese J. Math. 26 (4) 741 - 763, August, 2022. https://doi.org/10.11650/tjm/220107
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