Large-time asymptotics for nonlinear diffusions: the initial-boundary value problem
Francesco Salvarani, Giuseppe Toscani · Journal of Mathematical Physics · 2005
In this paper we investigate the large-time behavior of solutions to the first initial-boundary value problem for the nonlinear diffusion ut=(um)xx,m>0. In particular, we prove exponential decay of u(x,t) towards its own steady state in L1-norm for long times and we give an explicit upper bound for the rate of decay. The result is based on a new application of entropy estimates, and on detailed lower bounds for the entropy production in this situation.