Hello,

I am considering the following non-linear heat equation

$$ \left(\frac{\partial}{\partial t}-\nu\: \Delta \right) u(t,x) = F(t,x) \sigma(u(t,x)),\qquad (t,x)\in R_+\times R^d $$ where $F(t,x)$ is certain external heat source and $\sigma$ is a Lipschitz continuous function. Let's call $\nu$ the diffusion coefficient. When I calculate certain properties of the above equation, I find that when $d=1$, the results do not depend on the value of $\nu$, however when $d\ge 2$, the value $\nu$ becomes important. In particular, for the properties that I am studying, we need that $\nu > 1/(2\pi)$ !?.. Does anyone have ever had such critical dependence on $\nu$? Or does anyone know any phenomenon (like phase transitions) depending on $\nu$?

Thank you very much for any hints!

Anand

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