一类有边界记忆条件的非线性波动方程解的整体存在和一致衰减

Global Existence and Uniform Decay of Solutions for a Nonlinear Wave Equation with Memory Condition at the Boundary

研究一类带记忆边界条件的科尔霍夫型波方程,主要讨论其整体解的存在唯一性及能量的衰减性.利用Galerk in近似方法研究方程解的存在唯一性,然后引入松驰函数,利用扰动能量方法证明系统能量的衰减.

A class of nonlinear wave equations of Kirehhoff type with memory condition at the boundary are discussed in this paper. The existence and uniqueness of global solutions for the equations are established by Galerkin＇s approximation method. Then, by using of perturbed energy method it is proved that the energy decay has the same rate as that of the relaxation function.