Global Solutions to an Initial Boundary Value Problem for the Mullins Equation

Abstract

In this article we study the global existence of solutions to an initial boundary value problem for the Mullins equation which describes the groove development at the grain boundaries of a heated polycrystal, both the Dirichlet and the Neumann boundary conditions are considered. For the classical solution we also investigate the large time behavior, it is proved that the solution converges to a constant, in the L^∞(Ω)-norm, as time tends to infinity.