Special Session 7: Emergence and Dynamics of Patterns in Nonlinear Partial Differential Equations and Related Fields
Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation
Morgan Pierre
Universite de Poitiers France
Co-Author(s): Matthieu Brachet and Philippe Parnaudeau
Abstract:
We review space and time discretizations of the Cahn-Hilliard equation which are energy stable. In many cases, we prove that a solution converges to a steady state as time goes to infinity. The proof is based on Lyapunov theory and on a Lojasiewicz type inequality. In a few cases, the convergence result is only partial and this raises some interesting questions.