Invariant Manifolds and Grobman-Hartman Theorem for Equations with Degenerate Operator at the Derivative

机译：导数上具有简并算子的方程的不变流形和Grobman-Hartman定理

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Analog of Grobman-Hartman theorem about stable and unstable manifolds solutions for differential equations in Banach spaces with degenerate Fredholm operator at the derivative are proved. In contrast to usual evolution equation here central manifold arises even in the case of spectrum absence on the imaginary axis. Jordan chains tools and implicit operator theorem are used. The obtained results allow to develop center manifold methods for computation of bifurcation solution asymptotics and their stability investigation.

机译：证明了Banach空间中微分方程的稳定和不稳定流形解的Grobman-Hartman定理的类比，并用简并的Fredholm算子表示。与通常的演化方程相反，即使在虚轴上频谱不存在的情况下，中心流形也会出现。使用约旦链工具和隐式算子定理。获得的结果允许开发中心歧管方法来计算分叉溶液渐近性及其稳定性研究。

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《International Conference on Computational Science - ICCA 2003 Pt.2 Jun 2-4, 2003 Melbourne, Australia and St. Petersburg, Russia》|2003年|p.533-541|共9页
会议地点 Melbourne(AU) St. Petersburg(RU);Melbourne(AU) St. Petersburg(RU)
作者
Buelent Karasoezen; Irina Konopleva; Boris Loginov;
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作者单位

Ankara Middle-East Technical University, 06531 Ankara, Turkey;

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原文格式 PDF
正文语种 eng
中图分类自动化技术、计算机技术;
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3. LOCAL EXISTENCE THEOREMS WITH UNBOUNDED SET OF INPUT DATA AND UNBOUNDEDNESS OF STABLE INVARIANT MANIFOLDS FOR 3D NAVIER-STOKES EQUATIONS [J] . Andrei Fursikov Discrete and continuous dynamical systems▼hSeries S . 2010,第2期

机译：输入数据无界的局部存在定理和3D Navier-Stokes方程的稳定不变流形的无界性
4. Invariant Manifolds and Grobman-Hartman Theorem for Equations with Degenerate Operator at the Derivative [C] . International conference on computational science . 2003

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5. Invariant manifolds, invariant foliations and linearization theorems in Banach spaces. [D] . Tan, Bin. 1998

机译：Banach空间中的不变流形，不变叶面和线性化定理。
6. EIGENFUNCTION EXPANSIONS FOR SINGULAR ELLIPTIC OPERATORS. II. THE HILBERT SPACE ARGUMENT; PARABOLIC EQUATIONS ON OPEN MANIFOLDS [O] . Felix E. Browder 1954

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7. Harnack inequalities and B\^ocher-type theorems for conformally invariant fully nonlinear degenerate elliptic equations [O] . Li, YanYan, Nguyen, Luc 2013

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8. Linearisation Along Invariant Manifolds and a Generalisation of the Hartman-Grobman Theorems for Degenerate Singularities of Vectorfields in (Rsup 3) [R] . van Strien, S. 1987

机译：沿着不变流形的线性化和（Rsup 3）中矢量场退化奇性的Hartman-Grobman定理的推广

Invariant Manifolds and Grobman-Hartman Theorem for Equations with Degenerate Operator at the Derivative

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