关于非线性初边值问题的奇摄动(Ⅱ)

On Singular Perturbation for a Nonlinear initial-Boundary Value Problem (Ⅱ)

本文研究一类拟线性双曲—抛物型方程,具有变动边界的初边值问题的奇摄动:在某些条件成立,且ε充分小时,此问题的解具有以退化问题充分光滑解为首项的广义渐近展开式(Van der Corput意义),它在充分光滑解存在的区域Q={(x,t)|l_0(t)≤x≤l_1(t),0≤t≤T}上一致有效.其边界层存在于t=0附近.本文是工作[3]～[5]的进一步发展.

In this paper, we consider a singularly perturbed problem of a kind of qu si-linear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary. When certain assumptions are satisfied and e is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solution exists. The layer exists in the neighborhood of t=0. This paper is the development of references[3]~[5] .