Extended solutions for general fast diffusion equations with optimal measure data (Q930311)

Let \((N-2)_+/N<m_1\leq m_2<1\). The authors prove the existence of nonnegative solutions for the Cauchy problem \(u_t=\Delta\varphi(u)\) in \(\mathbb R^N\times(0,\infty)\), \(u(\cdot,0)=\nu\), where \(\nu\) is a nonnegative Borel measure and \(\varphi:\mathbb R_+\to\mathbb R_+\) is continuous, increasing and \(m_1\leq s\varphi'(s)/\varphi(s)\leq m_2\) for all \(s>0\). If \(\varphi\) is concave then they also prove uniqueness and study the asymptotic behavior of solutions.