Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 76, pp. 1-10.
Title: Blowup and asymptotic stability of weak solutions to wave
equations with nonlinear degenerate damping and source terms
Authors: Qingying Hu (Henan Univ., Zhengzhou, China)
Hongwei Zhang (Henan Univ., Zhengzhou, China)
Abstract:
This article concerns the blow-up and asymptotic
stability of weak solutions to the wave equation
$$
u_{tt}-\Delta u +|u|^kj'(u_t)=|u|^{p-1}u
\quad \hbox{in }\Omega \times (0,T),
$$
where $p>1$ and $j'$ denotes the derivative of a $C^1$ convex
and real value function $j$.
We prove that every weak solution is asymptotically stability,
for every $m$ such that $0k+m$ and
the initial data is positive, but appropriately bounded.
Submitted February 27, 2007. Published May 22, 2007.
Math Subject Classifications: 35B40.
Key Words: Wave equation; degenerate damping and source terms;
asymptotic stability; blow up of solutions.