The global existence and finite time extinction of a quasilinear parabolic equation
This paper is concerned with the existence of various positive self-similar solutions of the fast diffusion equation \(u_t = \text{div} (|\nabla u|^{m-1}\nabla u)\) in \(\mathbb{R}^n\times (0,\infty)\) with \(0 < m < 1\), \(n\geq 2\). It is proven that there exist both global and finite time extinction self-similar solutions under appropriate conditions on \(m\) and \(n\). The authors give a detailed information on asymptotic properties of such solutions as \(|x|\) tends to \(\infty\).
scientific article; zbMATH DE number 1493609