一类非线性双曲方程初边值问题整体解的衰减

Energy decay of global solution of initial boundary value problem for a class of nonlinear hyperbolic equation

利用能量扰动法研究了一类非线性双曲方程utt-uxxt=f(ux)x的混合初边值问题整体解的衰减性,分别得到了f′(s)≥γ>0和f(s)=|s|α-2s两种情形下整体解的指数衰减性和多项式衰减性.

The energy decay for an initial boundary value problem of the nonlinear hyperbolic equation uu - uxxt =f（ux ）x is studied by using a so-called energy perturbation method. The exponential decay of solution for the casef（s）≥7 〉0 and the algebraic decay of solution for the case f（s） = ｜s｜^a-2s are proved respectively.