Large time behaviour of higher dimensional logarithmic diffusion equation

Kin Ming Hui, Sunghoon Kim

Let $n\ge 3$ and ${\psi }_{{\lambda }_0}$ be the radially symmetric solution of $\Delta \log \psi +2\beta \psi +\beta x\cdot \nabla \psi =0$ in $R^n$, $\psi (0)={\lambda }_0$, for some constants ${\lambda }_0>0$, $\beta >0$. Suppose $u_0\ge 0$ satisfies…