ON THE SLOW DYNAMICS FOR THE CAHN-HILLIARD EQUATION IN ONE SPACE DIMENSION

we study the limiting behaviour of the solution of the Cahn-Hilliard equation using 'energy-type methods'. We assume that the initial data has a 'transition layer structure', i.e. u(epsilon) almost-equal-to +/- 1 except near finitely many transition points. We show than, in the limit as epsilon --> 0, the solution maintains its transition layer structure, and the transition layers move slower than any power of epsilon.