Lower bounds for the blow-up time to a nonlinear viscoelastic wave equation with strong damping

Abstract This paper deals with a nonlinear viscoelastic wave equation with strong damping. Under certain conditions on the initial data and the relaxation function, a lower bound for the blow-up time is given by means of a first order differential inequality technique.

[1]  Marco Squassina,et al.  Global solutions and finite time blow up for damped semilinear wave equations ? ? The first author w , 2006 .

[2]  Salim A. Messaoudi,et al.  Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation , 2006 .

[3]  Fang Liu,et al.  A lower bound for the blow-up time to a viscoelastic hyperbolic equation with nonlinear sources , 2016, Appl. Math. Lett..

[4]  Salim A. Messaoudi,et al.  Blow up and global existence in a nonlinear viscoelastic wave equation , 2003 .

[5]  Khadijeh Baghaei,et al.  Lower bounds for the blow-up time in a superlinear hyperbolic equation with linear damping term , 2017, Comput. Math. Appl..

[6]  Bin Guo,et al.  A lower bound for the blow-up time to a damped semilinear wave equation , 2014, Appl. Math. Lett..

[7]  Vladimir Georgiev,et al.  Existence of a Solution of the Wave Equation with Nonlinear Damping and Source Terms , 1994 .

[8]  Haitao Song,et al.  Blow up in a nonlinear viscoelastic wave equation with strong damping , 2014 .

[9]  Salim A. Messaoudi,et al.  Blow Up in a Nonlinearly Damped Wave Equation , 2001 .

[10]  Gérard A. Philippin,et al.  Lower bounds for blow-up time in a class of nonlinear wave equations , 2015 .

[11]  Chengkui Zhong,et al.  Blow-up of solutions of a nonlinear viscoelastic wave equation☆ , 2010 .

[12]  Howard A. Levine,et al.  Global Nonexistence Theorems for Quasilinear Evolution Equations with Dissipation , 1997 .

[13]  Guo Zhenhua,et al.  Lower bounds for blow-up time of a nonlinear viscoelastic wave equation , 2015 .

[14]  Enzo Vitillaro,et al.  Global Nonexistence Theorems for a Class of Evolution Equations with Dissipation , 1999 .