Convergence to equilibrium for the semilinear parabolic equation with   dynamical boundary condition
  This paper is concerned with the asymptotic behavior of the solution to the semilinear parabolic equation with dynamical boundary condition. Our main goal is to prove the convergence of a global solution to an equilibrium as time goes to infinity by means of a suitable \L ojasiewicz--Simon type inequality. 
Hao Wu
math.AP