  We present a general method for studying long time asymptotics of nonlinear
parabolic partial differential equations. The method does not rely on a priori
estimates such as the maximum principle. It applies to systems of coupled
equations, to boundary conditions at infinity creating a front, and to higher
(possibly fractional) differential linear terms. We present in detail the
analysis for nonlinear diffusion-type equations with initial data falling off
at infinity and also for data interpolating between two different stationary
solutions at infinity.
