Uniqueness of the Critical Rayleigh and Wave Numbers for the Inhomogeneous Planar Benard Problem
Matthew Glomski, Brian Hassard · 2011
The neutral stability equation F(k,R) = 0 for the inhomogeneous planar Benard problem is studied. Using analytical techniques and methods of verified interval computations, it is proved that the solu- tion set Rj (k) to the equation is a collection of curves with a least curve R1(k). Further, it is proved that the curve R1(k) attains a unique minimum at a critical wave number and Rayleigh number (k∗,R∗). Mathematics Subject Classification: 76E06, 65G20, 37M20