Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao, Takaaki Nishida:
A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem,
Journal of Mathematical Fluid Mechanics, Vol.6, No.1 (2004) pp.1-20.
A computer assisted proof of bifurcated steady-state solutions for the
two-dimensional Rayleigh-B\'enard convection is described.
The method is based on an infinite dimensional fixed-point theorem using
a Newton-like operator. This paper also proposes a numerical verification
algorithm which generates automatically on a computer a set including the
exact nontrivial solution. All discussed numerical examples take into
account of the effects of rounding errors in the floating point computations.
The publisher holds the copyright on this manuscript.