Existence and long-time behaviour of weak solutions for the Mullins equation

We study the initial–boundary value problem for the fourth order Mullins equation with initial data h0∈W11(Ω) under an assumption that the specific free energy of the boundary is less than the surface free energy. The model that we study was derived by Mullins in 1957 to analyse the time-evolution of surface grooves at the grain boundaries of heated polycrystal. We prove global in time existence of weak solutions and we also show that the energy minimizing steady state is the global attractor.