Existence and asymptotic stability of solutions for a hyperbolic equation with logarithmic source. Issue 4 (4th March 2023)

• Record Type: Journal Article
• Authors: Ha, Tae Gab
• Is Part Of: Applicable analysis. Volume 102:Issue 4(2023)
• Page Start: 1144
• Page End: 1160
• Publication Date: 2023-03-04
• Subjects: Logarithmic source -- existence of solutions -- energy decay rate; 35L71 -- 35A01 -- 35B35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1979216
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we consider a hyperbolic equation with a logarithmic source term. This work is devoted to prove the global existence and the uniform energy decay rates of a weak solution applying the logarithmic Sobolev inequality and modified multiplier method. This result gives us to classify the energy decay rate dependent on the growth near zero on the damping term.