Long time behaviour of a singular phase transition model
Pavel Krejčı́, Jürgen Sprekels · Discrete and Continuous Dynamical Systems · 2006
A phase-field system, non-local in space and non-smooth in time, with heat flux proportional to the gradient of the inverse temperature, is shown to admit a unique strong thermodynamically consistent solution on the whole time axis. The temperature remains globally bounded both from above and from below, and its space gradient as well as the time derivative of the order parameter asymptotically vanish in $L^2$-norm as time tends to infinity.