Asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case
A drift-diffusion system of mean field type involving singular diffusion \(\Delta u^\alpha\), \(1-1/n<\alpha<1\), and a nonlocal transport term is considered in \(\mathbb R^n\), \(n\ge 3\). The main result is that the asymptotically long time behavior of global-in-time solutions is described by generalized Barenblatt self-similar solutions. Rényi type entropy functional is used together with suitable a~priori estimates.
scientific article; zbMATH DE number 7433260
scientific article