Asymptotic Solution of a Nonlinear Initial-Boundary Value Problem for the Diffusion Equation with a Small Parameter Multiplying the Time Derivative

被引：0

作者：

Belolipetskii A.A. ^{[1
]}

Malinina E.A. ^{[1
]}

机构：

[1] Moscow State University, Moscow

来源：

Computational Mathematics and Modeling | 2014年 / 25卷 / 1期

关键词：

Banach space; boundary-value problem; integral equation; parabolic equation; shell; small parameter;

D O I：

10.1007/s10598-013-9204-z

中图分类号：

学科分类号：

摘要：

We prove the existence and construct the form of the asymptotic solution for an initial-boundary value problem that describes diffusive filling of thin shells with a real gas. Such problems arise in the manufacturing of laser targets, where a thin spherical shell is filled with hydrogen isotopes to a high pressure [1-3]. In this article we apply the methods of [4], but the nonlinearity of the boundary conditions requires new approaches to the problem. © 2013 Springer Science+Business Media New York.

引用

页码：9 / 26

页数：17

共 6 条

[1]

Aleksandrova I.V., Belolipetskii A.A., Koresheva E.E., Cryogenic Reactor Targets, Part 1: Diffusive Filling of Spherical Shells [in Russian], (2012)

[2]

Belolipetskii A.A., Semenov K.O., Investigation of a mathematical model of filling a two-layer porous shells with gas, Vest. MGU, Zer. 15: Comput. Math. Cybernetics, 4, pp. 3-10, (2011)

[3]

Aleksandrova I.V., Belolipetskiy A.A., Mathematical models for filling polymer shells with a real gas fuel, Laser Particle Beams, 17, 4, pp. 701-712, (1999)

[4]

Belolipetskii A.A., Ter-Krikorov A.M., Solution of a singularly perturbed initial-boundary value problem for a linear parabolic equation, Trudy MFTI, 3, 1, pp. 4-17, (2011)

[5]

Ter-Krikorov A.M., Nonlinear Analysis and Asymptotic Small-Parameter Methods: A Textbook [in Russian], (2007)

[6]

Kato T., Perturbation Theory for Linear Operators [Russian Translation], (1972)

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