Global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity. (July 2019)

• Record Type: Journal Article
• Authors: Lian, Wei; Ahmed, Md Salik; Xu, Runzhang
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 239
• Page End: 257
• Publication Date: 2019-07
• Subjects: Global existence -- Infinite time blow up -- Logarithmic nonlinearity -- Potential well; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.02.015
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider the semilinear wave equation with logarithmic nonlinearity. By modifying and using potential well combined with logarithmic Sobolev inequality, we derive the global existence and infinite time blow up of the solution at low energy level E ( 0 ) < d . Then these results are extended in parallel to the critical case E ( 0 ) = d . Besides, with additional assumptions on initial data, the infinite time blow up result is given with arbitrary positive initial energy E ( 0 ) > 0 .