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

Xiaoming Peng; Xiaoxiao Zheng; Yadong Shang

doi:10.3934/Math.2018.4.514

AIMS Mathematics, 2018, 3(4): 514-523. doi: 10.3934/Math.2018.4.514. Research article

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

Xiaoming Peng, Xiaoxiao Zheng, Yadong Shang

¹ School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China
² School of Mathematical Sciences, Qufu Normal University, Qufu 273155, Shandong, China
³ School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

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This paper deals with a nonlinear viscoelastic wave equation with strong damping. By the means of the interpolation inequalities and di erential inequality technique, we obtain a lower bound for blow-up time of the solution. This result extends our earlier work Peng et al. [Appl. Math. Lett., 76, 2018].

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Keywords: lower bound; blow up; viscoelastic; strong damping; memory

Citation: Xiaoming Peng, Xiaoxiao Zheng, Yadong Shang. Lower bounds for the blow-up time to a nonlinear viscoelastic wave equation with strong damping. AIMS Mathematics, 2018, 3(4): 514-523. doi: 10.3934/Math.2018.4.514

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