On the global solvability of porous media type equations with space dependent advection flux

Abstract

We show that the Cauchy problem for advection-diffusion equations with nonlinear diffusion term div(|u|α∇u) and advection flux f(x,t,u) of order O(|u|1+k) for large u is globally solvable for arbitrary initial data u0∈L1(Rn)∩L∞(Rn) when k∈[0,α+1/n). Some important related results are also given.