Existence and uniqueness of the solution of the boundary-value problem for a parabolic equation of unsteady filtration

被引：16

作者：

Kazakov, A. L. ^{[1
]}

Lempert, A. A. ^{[1
]}

机构：

[1] Russian Acad Sci, Inst Syst Dynam & Control Theory, Siberian Branch, Irkutsk 664033, Russia

来源：

JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS | 2013年 / 54卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

nonlinear filtration; partial differential equations; boundary-value problem; existence and uniqueness theorem; series; convergence;

D O I：

10.1134/S0021894413020107

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

The problem of the motion of a filtration front in a zero background in the case of a power-law dependence of the filtration coefficient on gas density is considered, and the existence and uniqueness theorem for solutions in the class of analytic functions is proved. The solution is constructed in explicit form, recurrence formulas for computing the coefficients in the series are obtained, and the convergence of the series is proved by the majorant method. The filtration front construction procedure is proposed.

引用

页码：251 / 258

页数：8

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