双曲-抛物奇异摄动问题的O（ε^n）阶渐近展开

An Asymptotic Expansion for Quasi-liner Singular Perturbation Problem of Hyperbolic-Parabolic Partial Differential Equation

为讨论一个双曲-抛物奇异摄动问题的渐近展开问题,首先用能量方法建立稳定不等式,然后利用双重迭代法对原问题进行渐近展开,最后用稳定不等式证明了渐近解对原问题解的O(εn)阶逼近式,从而证明了渐近解的一致有效性.

A singular perturbation problem of a hyperbolic-parabolic partial differential equation is dis- cussed. In order to solve the asymptotic expansion of the problem, the energy method is applied to establish the continuous stability inequality and the n-order asymptotic expansion of the solution to this problem with respect to small parameters. Thus the uniform effectiveness of the asymptotic expansion is proved.