Yoshitaka Watanabe and Mitsuhiro T. Nakao:
Numerical Verification Method of Solutions for Elliptic Equations and Its Application to the Rayleigh-Bénard Problem,
Japan Journal of Industrial and Applied Mathematics, Vol. 26, No. 2-3 (October 2009) pp. 443-463.

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.

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