Phase transitions and symmetry breaking in singular diffusion.
The long-time asymptotics are determined for fast nonlinear diffusion by linearizing Otto's gradient descent model at the Barenblatt profile. The spectrum of the entropy is explicitly determined. The dynamics are found to undergo a phase transition in which rotational symmetry is broken as the strength of the nonlinearity is varied.
Denzler
Jochen
J
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USA.
McCann
Robert J
RJ