高阶椭圆型方程第一边值问题的奇摄动(Ⅱ)
Singular Perturbation of First Boundary Value Problem for Higher Order Elliptic Equations (Ⅱ)
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摘要: 本文研究含双参数的高阶椭圆型方程第一边值问题的奇摄动,得到包含两个形式参数的渐近解表达式,并对余项进行估计,拓广了文[2]、[3]的结果.Abstract: In this paper we discuss singular perturbations of first boundary value problem for higher order elliptic equations of two parameter and obtain the asymptotic expression for the formal solution containing two-parameter.
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[1] Zheng Yong-shu,Singular perturbation of first boundary value problem for higher order elliptic equation(I),Transactions of Fukien Teachers'University,1(1980),9-22.(in Chinese) [2] Вишик.М.И.и Люстерник.Л.А.,Регулярное вырожденеие и пограниый слойдля линейных дифферевдиалъных равнений с малым дараметром УМН 12,5(1957),3-122. [3] Вишик.М.И.и Люстерник.Л.А.,Решение некоторых задач о вознушении вслучяе матрип и самосопряженных и несамосопряжеынных дифференпиалъных уравнений ⅠУМН15,5(1960),3-80. [4] Besjes,J.G.,Singular perturbation problems for linear elliptic differential operators of arbitrary order,J.Math.Anal,and Appl.,Vol.49,No.1(1975),24-46. [5] Nirenberg.L.,Estimates and existence of solution of elliptic equations,Comm.Pure Appl.Math.Vol.9(1956),509-530.
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