On the existence of solutions of the Cauchy problem for porous medium equations with radon measure as initial data (Q1355019)

The author studies the Cauchy problem for the general porous medium equation \(u_t-\Delta\Phi(u)= 0\) on \(\mathbb{R}^n\times (0,T)\) with a nonnegative Radon measure as initial condition. Here \(\Phi'(s)\) roughly behaves like \(\ln(1+ s)^m\), where \(m\) is arbitrary, thereby generalizing slightly the assumption of \textit{D. Andreucci} and \textit{E. Di Benedetto} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7, No. 4, 305-334 (1990; Zbl 0723.35014)]. Global existence for \(m<-1\) and local existence for \(m\geq -1\) under additional growth assumptions on the initial trace is proved.