I am working on estimating norms of solutions of the simplified version of the Fokker-Planck equation$$ u_t=\text{div}(b(x)u)+\text{div}(a(x)\nabla u) $$ with $\text{div}\in L^q(\mathbb{R}^d)$ using mainly Functional Analysis inequalities. I was computing the ratio between powers of norms of the solution when suddenly the following number appears$$ \frac{3+\sqrt{5}}{2} $$ Is this number somehow important, other than it's the goldent ratio plus $1$? And how does that number even appear on Functional Analysis or PDE?

I know I did not give the full details of my work (it is rather extensive), but I was quite surprised and curious. Any ideas?

  • 3
    $\begingroup$ Could you possibly show the specific part that got you the number? What specific numbers gave you the ratio and how did you get them? For instance, it shows up as $\phi+1=\lim_{n\to\infty}\frac{F_{n+2}}{F_n}$ Also, $\phi^2=\phi+1$, so it's also the golden ratio squared. $\endgroup$ – AlgorithmsX Feb 6 '18 at 20:08

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