Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems
Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems
复制标题
非线性热对流问题分叉解的计算机辅助证明
DOI：
--
复制
发表时间：
2010
影响因子：
2.5
通讯作者：
Myoungnyoun Kim
中科院分区：
文献类型：
--
作者：
M. Nakao;Yoshitaka Watanabe;N. Yamamoto;T. Nishida;Myoungnyoun Kim
在之前的工作中（Nakao et al., Reliab. Comput., 9(5):359–372, 2003；Watanabe et al., J. Math. Fluid Mech., 6(1):1–20, 2004），作者考虑了二维热对流问题（称为瑞利-贝纳德问题）解的数值验证方法。在本文中，为了使论点自成一体，我们首先总结这些结果，包括用数值例子对问题的基本表述。接下来，我们将给出一种验证分叉点本身的方法，这应该是阐明全局分叉结构的重要信息，并给出一个数值示例。最后，将描述对三维情况的扩展。
In previous works (Nakao et al., Reliab. Comput., 9(5):359–372, 2003; Watanabe et al., J. Math. Fluid Mech., 6(1):1–20, 2004), the authors considered the numerical verification method of solutions for two-dimensional heat convection problems known as Rayleigh-Bénard problem. In the present paper, to make the arguments self-contained, we first summarize these results including the basic formulation of the problem with numerical examples. Next, we will give a method to verify the bifurcation point itself, which should be an important information to clarify the global bifurcation structure, and show a numerical example. Finally, an extension to the three dimensional case will be described.