Asymptotic behavior of solution to the Cahn-Hillard equation

Abstract

The asymptotic behavior of solution to the initial boundary value problem of nonlinear Cahn-Hilliard equation and the associated stationary problem have been extensively studied. In particular, it is proved that in the one space dimensional case the associated stationary problem has exactly 2N+1 numbers of solutions and the solution of evolution equation converges to certain equilibrium solution as t→+∞.

AMS (MOS):

• 35B40

^{*On leave from Institute of Mathematics, Fudan University Shanghai, China. This work was partially supported by the National Science Foundation, Grant No. DMS-8501397 and the Air Force Office of Scientific Research.}

^{*On leave from Institute of Mathematics, Fudan University Shanghai, China. This work was partially supported by the National Science Foundation, Grant No. DMS-8501397 and the Air Force Office of Scientific Research.}

Notes

^{*On leave from Institute of Mathematics, Fudan University Shanghai, China. This work was partially supported by the National Science Foundation, Grant No. DMS-8501397 and the Air Force Office of Scientific Research.}