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)
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摘要: 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)|l0(t)≤x≤l1(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.Abstract: In this paper, we consider a singularly perturbed problem of a kind of quasilinear 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].
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Key words:
- singular perturbation /
- m oving boundary /
- asy m ptotic ezpansion
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[1] Zlamal,M.,On mixed problem for a hyperbolic equation with a small parameter,J,Math,Czechoslovakia,9(94)(1959). [2] 江福汝.含小参数的双曲型方程的混合问题,复旦大学《数学论文集》(1962),52-60 [3] 高汝熹.拟线性双曲型方程的奇摄动.数学年刊.4B(3)(1983),293-298. [4] 康连城,一类拟线性双曲一抛物型方程混合问题的奇摄动.数学年刊.gA(6)(1985),707-714. [5] 康连城.关于非线性初边值问题的奇摄动(I).数学年刊,10A(5)(1989),529-531. [6] 江福汝.关于边界层方法.应用数学和力学,2(5)(1981),461-474. [7] Van der Corput,J. G,,.Asymptotic development,I,J,Anal,Math.,4(1955),341-418. [8] 周毓麟,非线性抛物型方程的边界问题,Maine Cδo.,47(89)4(1959),431-484(CCCP) [9] 许克明,非线性抛物型方程的一类边值问题,数学研究与评论,7(2)(1987),277-282. -
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