Cahn-Hilliard equations with inertial term
by
Maurizio Grasselli
Dipartimento di Matematica - Politecnico di Milano

The Cahn-Hilliard equation is a nonlinear first-order evolution equation which plays an important role in Materials Sciences since it models phase-separation phenomena in binary mixtures. A typical feature of such processes is the so-called spinodal decomposition, i.e., a situation in which both the phases have an equivalent symmetry and differ only in composition. To give a better description of spinodal decomposition n certain materials like glasses, some physicists have recently proposed to add an inertial term into the original equation which thus becomes a second-order evolution equation. This modification can be viewed as a singular perturbation of the standard Cahn-Hilliard equation, when the inertial coefficient is small. I will illustrate some of the mathematical aspects of this second-order equation. More precisely, I will mainly focus on the large time behavior of solutions, speaking of global and exponential attractors as well as of convergence of a solution to equilibrium. In addition, I will compare quantitatively the solutions to the Cahn-Hilliard equation with the ones solving its singular perturbation.

Date received: February 21, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawu-05.