Asymptotic analysis of a doubly nonlinear diffusion equation. (June 2016) - King, J.R.
Abstract: We investigate the doubly nonlinear diffusion equation ∂ u ∂ t = 1 n ∇ . ( u m | ∇ 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 < 0, that seem to us worthy of further mathematical investigation.