| DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS |
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| 作者姓名： | MA Tian WANG Shouhong |
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| 作者单位： | MA Tian WANG Shouhong Department of Mathematics，Sichuan University，Chengdu 610064，China; Department of Mathematics，Indiana University，Bloomington，IN 47405，USA. Department of Mathematics，Indiana University，Bloomington，IN 47405，USA. |
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| 基金项目： | Project supported by the O?ce of Naval Research, the National Science Foundation, and the NationalNatural Science Foundation of China (No.19971062). |
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| 摘 要： | §1. IntroductionA key problem in the study of problems in mathematical physics and mechanics is tounderstand and predict patterns and their transitions/evolutions. In ?uid mechanics, forinstance, it is important to study the periodic, quasi-periodic, ape…
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| 关 键 词： | 动力分支 稳定态 非线性演化方程 临界参数 希尔伯特空间 |
| 收稿时间： | 5/4/2024 12:00:00 AM |
DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS |
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| MA Tian,WANG Shouhong.DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS[J].Chinese Annals of Mathematics,Series B,2005,26(2):185-206. |
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| Authors: | MA Tian and WANG Shouhong |
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| Institution: | 1. Department of Mathematics,Sichuan University,Chengdu 610064,China;Department of Mathematics,Indiana University,Bloomington,IN 47405,USA
2. Department of Mathematics,Indiana University,Bloomington,IN 47405,USA |
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| Abstract: | The authors introduce a notion of dynamic bifurcation for nonlinear evolution equa- tions, which can be called attractor bifurcation. It is proved that as the control pa- rameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m 1, where m 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a uni?ed point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics. |
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| Keywords: | Attractor bifurcation Steady state bifurcation Dynamic bifurcation Hopf bifurcation Nonlinear evolution equation |
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