Communications on Pure and Applied Analysis (CPAA)

Asymptotic behavior of solutions to the phase-field equations with neumann boundary conditions

Pages: 683 - 693, Volume 4, Issue 3, September 2005      doi:10.3934/cpaa.2005.4.683

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Zhenhua Zhang - Institute of Mathematics, Fudan University, Shanghai 200433, China (email)

Abstract: This paper is concerned with the asymptotic behavior of solutions to the phase-field equations subject to the Neumann boundary conditions where a Lojasiewicz-Simon type inequality plays an important role. In this paper, convergence of the solution of this problem to an equilibrium, as time goes to infinity, is proved.

Keywords:  Phase-field equations, Lojasiewicz-Simon type inequality, gradient system.
Mathematics Subject Classification:  Primary: 35B40; Secondary: 35K20.

Received: September 2004;      Revised: May 2005;      Available Online: June 2005.