Electron. J. Diff. Equ., Vol. 2015 (2015), No. 306, pp. 1-12.

Blow-up for the Euler-Bernoulli viscoelastic equation with a nonlinear source

Zhifeng Yang, Guobing Fan

Abstract:
In this article, we consider the Euler-Bernoulli viscoelastic equation
$$ u_{tt}(x,t)+ \Delta^2 u(x,t)-\int_0^t g(t-s)\Delta^2 u(x,s)ds=|u|^{p-1}u $$
together with some suitable initial data and boundary conditions in $\Omega\times (0,+\infty)$. Some sufficient conditions on blow-up of solutions are obtained under different initial energy states. And from these results we can clearly understand the competitive relationship between the viscoelastic damping and source.

Submitted September 1, 2015. Published December 16, 2015.
Math Subject Classifications: 35L35, 35G16.
Key Words: Viscoelastic equation; blow-up; nonlinear source.

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Zhifeng Yang
College of Mathematics and Computer Science
Hunan Normal University
Changsha, Hunan, 410081, China
email: zhifeng_yang@126.com
Guobing Fan
Hunan University of Finance and Economics
Changsha, Hunan 410205, China
email: fan_guobing@126.com

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