Blow-up of solutions of a nonlinear viscoelastic wave equation

作者：Song, Haitao^*; Zhong, Chengkui

来源：Nonlinear Analysis: Real World Applications , 2010, 11(5): 3877-3883.

DOI：10.1016/j.nonrwa.2010.02.015

• Blow-up
• Finite time
• Hyperbolic
• Strong damping
• Positive initial energy
• Viscoelastic

In this paper, we consider the nonlinear viscoelastic equation
u(tt) - Delta u + integral(1)(0) g(t - tau)Delta u(tau)d tau - Delta u(t) =vertical bar u vertical bar(p-2)u, in Omega x [0, T],
with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g, we prove that there are solutions with positive initial energy that blow up in finite time.

• 出版日期2010-10
• 单位兰州大学