具有摩擦和记忆性的非线性波动方程一致能量衰减估计(英文)

Uniform Energy Decay Estimation for Nonlinear Wave Equation with Friction and Memory

考虑一类非线性粘弹性波动方程utt-κ0Δu+∫t0g(t-s)div[a(x)u(s)]ds+b(x)h(ut)=f(u),(x,t)∈Ω×(0,∞)的初边值问题.在对函数g,h和f比较弱的假设下,通过引入简单的Lyapunov泛函和精确先验估计证明了能量一致衰减.

In this paper we consider a class of nonlinear viscoelastic wave equation uu-κ0△u＋∫0g（t-s）div[a（x）△u（s）]ds＋b（x）h（ut）=f（u）,（x,t）∈Ω×（0,∞）with initial-boundary conditions. Under weaker assumptions on the functions g,h and f, the uniform energy decay are proved by introducing very simple Lyapunov functional and precise priori estimates.