Non-existence of fundamental solutions of the equation \(u_ t=\Delta \ln u\) (Q1323921)

We prove the non-existence of solutions for the equation \[ \begin{cases} \partial u/ \partial t = \Delta\ln u, & (x,t) \in\mathbb{R}^ n \times (0,\infty),\;n \geq 3\\ u(x,t) > 0 & \forall x \in\mathbb{R}^ n,\;t > 0\\ u(x,0) \to \delta_ 0 & \text{in \({\mathcal D}'(\mathbb{R}^ n)\),}\end{cases} \] where \(\delta_ 0\) is the delta mass at the origin.