拟线性双曲-抛物奇异摄动问题的O（ε^3）阶渐近展开

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

为讨论一个拟线性双曲—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O(ε3)逼近式,从而证明了渐近解的一致有效性.

A singular perturbation problem of a quasi-linear hyperbolic-parabolic partial differential equa-tion is discussed. In order to discuss the asymptotic expansion of the problem,the energy method is applied to establish the continuous stability inequality and the 3-order asymptotic expansion of the solution to this problem with respect to small parameters. Thus the uniform effectiveness of the asymptotic expansion is proved.