On the modified of the one-dimensional Cahn-Hilliard equation with a source term

Abstract

We consider the modified Cahn-Hilliard equation that govern the relative concentration $ \phi $ of one component of a binary system. This equation is characterized by the presence of the additional inertial term $ \tau_{D}\frac{d^2\phi}{dt^2} $ which stands for the relaxation of the diffusion flux. This equation is associated with Dirichlet boundary conditions. We study the existence, uniqueness and regularity of solutions in one space dimension. We also prove the existence of the global attractor and exponential attractors.

Keywords

• cahn-hilliard equation
• well posedness
• strongly continous semigroups
• globall attractors
• robust exponential attractors