Open AccessExistence and nonexistence of global solutions for logarithmic hyperbolic equation
Author(s) -
Yaojun Ye,
Quanxin Zhu
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022054
Subject(s) - mathematics , logarithm , sobolev space , mathematical analysis , hyperbolic partial differential equation , nonlinear system , boundary value problem , type (biology) , partial differential equation , physics , ecology , quantum mechanics , biology
This article is concerned with the initial-boundary value problem for a equation of quasi-hyperbolic type with logarithmic nonlinearity. By applying the Galerkin method and logarithmic Sobolev inequality, we prove the existence of global weak solutions for this problem. In addition, by means of the concavity analysis, we discuss the nonexistence of global solutions in the unstable set and give the lifespan estimation of solutions.