Global existence and uniform decay for wave equation with dissipative term and boundary damping

作者：Zhang, Zai-yun^*; Miao, Xiu-jin

来源：Computers & Mathematics with Applications, 2010, 59(2): 1003-1018.

DOI：10.1016/j.camwa.2009.09.008

• Wave equation
• Glerkin approximation
• Asymptotic behavior
• Boundary stabilization

In this paper,we prove the existence, uniqueness and uniform stability of strong and weak solutions of the nonlinear wave equation
u(tt) - Delta u + b(x)u(t) + f(u) = 0
in bounded domains with nonlinear damped boundary conditions, given by
partial derivative u/partial derivative v+g(u(t)) = 0,
with restrictions on function f(u), g(u(t)) and b(x),. We prove the existence by means of the Glerkin method and obtain the asymptotic behavior by using of the multiplier technique from the idea of Kmornik and Zuazua (see [7]).

• 出版日期2010-1
• 单位中南大学; 湖南理工学院