Open Access
Translator Disclaimer
August, 2022 Blow up and Decay for a Class of $p$-Laplacian Hyperbolic Equation with Logarithmic Nonlinearity
Ying Chu, Yuqi Wu, Libo Cheng
Author Affiliations +
Taiwanese J. Math. 26(4): 741-763 (August, 2022). DOI: 10.11650/tjm/220107


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).


We are very grateful to the anonymous referees for their valuable suggestions that improved the article.


Download 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.


Received: 11 October 2021; Revised: 18 January 2022; Accepted: 24 January 2022; Published: August, 2022
First available in Project Euclid: 23 February 2022

Digital Object Identifier: 10.11650/tjm/220107

Primary: 35A01 , 35B40 , 35B44 , 35L20

Keywords: $p$-Laplacian hyperbolic equation , blow up , energy decay estimates , global existence , logarithmic nonlinearity

Rights: Copyright © 2022 The Mathematical Society of the Republic of China


Vol.26 • No. 4 • August, 2022
Back to Top