System of Laplace equations in a half-space with a free interface, capillary-gravitational waves, bifurcation, and symmetry

被引：0

作者：

A. N. Andronov

机构：

[1] Mordovia State University,

来源：

Differential Equations | 2011年 / 47卷

关键词：

Jacobian Matrix; Laplace Equation; Invariant Manifold; Bifurcation Problem; Free Interface;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study the stability of branching solutions of a system of two nonlinearly perturbed Laplace equations in a half-space with two differential relations on the interface. This system describes the motion of a two-layer fluid. To construct and study the related branching systems, methods of group analysis of differential equations (RZhMat 1978 11B883K, RZhMat 1983 11A813K) and the S. Lie-L.V. Ovsyannikov technique of invariants and invariant manifolds are used.

引用

页码：758 / 763

页数：5

共 11 条

[1]

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[2]

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[3]

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[4]

Izakson V.Kh.(1971)The Use of Group Properties for the Determination of Multiparameter Families of Solutions of Nonlinear Equations Mat. Sb. 85 440-454

[5]

Yudovich V.I.(1975)The Use of Group Invariance in Branching Theory Differ. Uravn. 11 1518-1521

[6]

Loginov B.V.(1991)Generalized Jordan Structure in the Problem of the Stability of Bifurcating Solutions Nonlinear Anal. TMA 17 219-231

[7]

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