Abstract:

We used the LeraySchauder fixed point theorem to prove the existence of the classical solutions of the initial boundary
 value problem of one dimensional CahnHilliard equation with concentration dependent mobility and gradient dependent potential, and showed the uniqueness of the solutions by  means of Holmgren’s approach. In the case of one dimension, we generalized our previous work on the corresponding problem of the Cahn-Hilliard equation with constant mobility and gradient dependent potential.

Key words: CahnHilliard equation, concentration dependent mobility, gradient dependent potential, existence and uniqueness of solution