Asymptotic profile of solutions of a singular diffusion equation as \(t\to\infty\) (Q5960853)

The paper deals with the Cauchy problem NEWLINE\[NEWLINEu_t=\Delta \log u,\quad u>0\quad \text{in} {\mathbb R}^2\times(0,\infty),NEWLINE\]NEWLINE NEWLINE\[NEWLINEu(x,0)=u_0(x)\quad \text{for all }x\in {\mathbb R}^2.NEWLINE\]NEWLINE In another paper by the same author [Pac. J. Math. 197, 25-41 (2001; Zbl 1053.53045)] the large-time behaviour of solutions is studied. Namely, the solutions decay like \(|x|^{-2}\) as \(|x|\to\infty.\) Here, the author proposes a simplified proof of the same result.