Existence and nonexistence of global solutions for logarithmic
hyperbolic equation
- Yaojun YE
Yaojun YE
Zhejiang University of Science and Technology
Corresponding Author:yjye2013@163.com
Author ProfileAbstract
In this paper, we study the initial-boundary value problem of a class of
degenerate quasilinear hyperbolic equation with logarithmic
nonlinearity. By applying Galerkin method and the logarithmic Sobolev
inequality, we prove the existence of global weak solutions for this
problem. Meanwhile,the global nonexistence of solutions is verified by
means of the concavity analysis when the initial energy is positive and
appropriately bounded.2022Published in Electronic Research Archive volume 30 issue 3 on pages 1035-1051. 10.3934/era.2022054