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.
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.
"Blow up and Decay for a Class of $p$-Laplacian Hyperbolic Equation with Logarithmic Nonlinearity." Taiwanese J. Math. Advance Publication 1 - 23, 2022. https://doi.org/10.11650/tjm/220107