An asymptotic solution of the Dirichlet problem for the poisson equation on a nonperiodic frame

被引：0

作者：

Lapshin A.E.

Panasenko G.P.

机构：

来源：

Journal of Mathematical Sciences | 1997年 / 85卷 / 6期

基金：

俄罗斯基础研究基金会;

关键词：

Exact Solution; Asymptotic Expansion; Dirichlet Problem; Poisson Equation; Asymptotic Solution;

D O I：

10.1007/BF02355839

中图分类号：

学科分类号：

摘要：

In this paper, the Dirichlet problem for the Poisson equation is considered in a nonperiodic framelike domain that consists of thin short strips or cylinders. We construct a complete asymptotic expansion for the solution. We obtain an estimate for the difference between the exact solution and the asymptotic one. Bibliography: 9 titles. © 1997 Plenum Publishing Corporation.

引用

页码：2302 / 2307

页数：5

共 9 条

[1]

Panasenko G.P., The principle of splitting the homogenized operator for nonlinear systems in periodic and random framelike structures, Dokl. Akad. Nauk SSSR, 263, 1, pp. 35-40, (1982)

[2]

Bakhvalov N.S., Panasenko G.P., Homogenization of Processes in Periodic Media [in Russian], (1984)

[3]

Oleinik O.A., Yosifian G.A., Shamaev A.S., On the asymptotic expansion of solutions to the Dirichlet problem for elliptic equations and the elasticity theory system in a perforated domain, Dokl. Akad. Nauk SSSR, 284, 5, pp. 1062-1066, (1985)

[4]

Oleinik O.A., Shamaev A.S., Yosifian G.A., Mathematical Problems in Elasticity and Homogenization, (1992)

[5]

Marchenko V.A., Khruslov E.Ya., Boundary-value Problems in Domains with Fine-grained Boundaries [in Russian], (1974)

[6]

Lions J.L., Asymptotic expansions in perforated media with periodic structures, Rocky Mount. J. Math., 10, 1, pp. 125-140, (1980)

[7]

Landis E.M., Second-order Equations of Elliptic and Parabolic Types [in Russian], (1971)

[8]

Oleinik O.A., Yosifian G.A., On the behavior at infinity of solutions to second-order elliptic equations in domains with noncompact boundaries, Mat. Sb., 112, 4, pp. 588-610, (1980)

[9]

Oleinik O.A., Yosifian G.A., On the asymptotic behavior at infinity of solutions in linear elasticity, Arch. Rat. Mech. Anal., 78, 1, pp. 29-53, (1982)

← 1 →