Asymptotic stability of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order
In the present article we first study the existence of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order, which was proposed by Mullins ["Two-dimensional motion of idealized grain boundaries," J. Appl. Phys. 27, 900 (1956)] to describe the groove development, due to the surface diffusion, at the grain boundaries of a heated polycrystal. Then employing an energy method we prove that this stationary solution is asymptotically stable in a suitable norm as time goes to infinity. © 2009 American Institute of Physics.