Global existence and blow-up of solutions for higher-order viscoelastic wave equation with a nonlinear source term. (January 2015)

• Record Type: Journal Article
• Authors: Ye, Yaojun
• Is Part Of: Nonlinear analysis. Volume 112(2015)
• Page Start: 129
• Page End: 146
• Publication Date: 2015-01
• Subjects: Nonlinear higher-order viscoelastic wave equation -- Global existence -- Blow-up -- Lifespan estimate -- Nonlinear source term; 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.2014.09.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The initial–boundary value problem for some nonlinear higher-order viscoelastic wave equation with a nonlinear source term in a bounded domain is studied. The existence of global weak solutions for this problem is established by using the Galerkin method. Meanwhile, under suitable conditions on relaxation function g ( ⋅ ) and the positive initial energy as well as non-positive initial energy, it is proved that the solution blows up in the finite time and the lifespan estimates of solutions are also given.