Electron. J. Differential Equations, Vol. 2016 (2016), No. 332, pp. 1-8.

Blow-up of solutions for viscoelastic equations of Kirchhoff type with arbitrary positive initial energy

Zhifeng Yang, Zhaogang Gong

Abstract:
We consider the viscoelastic equation
$$ u_{tt}(x,t)-M(\|\nabla u\|_2^2) \Delta u(x,t)+\int_0^t g(t-s)\Delta u(x,s)ds+u_t =|u|^{p-1}u $$
with suitable initial data and boundary conditions. Under certain assumptions on the kernel g and the initial data, we establish a new blow-up result for arbitrary positive initial energy, by using simple analysis techniques.

Submitted June 2, 2016. Published December 28, 2016.
Math Subject Classifications: 35L05, 35L55, 35L70.
Key Words: Viscoelastic equation; blow-up; arbitrary positive initial energy.

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Zhifeng Yang
College of Mathematics and Statistics
Hengyang Normal University
Hengyang, Hunan, 421002, China
email: zhifeng_yang@126.com
Zhaogang Gong
College of Mathematics and Statistics
Hengyang Normal University
Hengyang, Hunan, 421002, China
email: zhaogang_gong@126.com

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