Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems
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- Nakao, M.T., Watanabe, Y., Yamamoto, N. et al. J Sci Comput (2010) 43: 388. doi:10.1007/s10915-009-9303-3
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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.