Longtime behavior for a nonlinear wave equation arising in elasto-plastic flow

✍ Scribed by Yang Zhijian

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 188 KB
• Volume: 32
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1080

✦ Synopsis

Abstract

The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a nonlinear wave equation arising in elasto‐plastic flow u~tt~−div{|∇u|^m−1^∇u}−λΔ__u__~t~+Δ^2^u+g(u)=f(x). It proves that under rather mild conditions, the dynamical system associated with above‐mentioned IBVP possesses a global attractor, which is connected and has finite Hausdorff and fractal dimension in the phase spaces X~1~=H(Ω) × L^2^(Ω) and X=(H^3^(Ω)∩H(Ω)) × H(Ω), respectively. Copyright © 2008 John Wiley & Sons, Ltd.