Asymptotic analysis of a doubly nonlinear diffusion equation

We investigate the doubly nonlinear diffusion equation ∂u∂t=1n∇.(um|∇u|n−1∇u) and the same equation expressed in terms of a ‘pressure’ variable. We classify various classes of compacted supported solutions, as well as finite-mass solutions that decay algebraically at infinity. A number of novel phenomena are identified, particularly for n<0n<0, that seem to us worthy of further mathematical investigation.