Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem

Article

Abstract

We first summarize the general concept of our verification method of solutions for elliptic equations. Next, as an application of our method, a survey and future works on the numerical verification method of solutions for heat convection problems known as Rayleigh-Bénard problem are described. We will give a method to verify the existence of bifurcating solutions of the two-dimensional problem and the bifurcation point itself. Finally, an extension to the three-dimensional case and future works will be described.

Key words

numerical verification method elliptic equations Rayleigh-Bénard problem bifurcation point 

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Copyright information

© JJIAM Publishing Committee 2009

Authors and Affiliations

  1. 1.Research Institute for Information TechnologyKyushu UniversityFukuokaJapan
  2. 2.Faculty of MathematicsKyushu UniversityJapan

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