AN ASYMPTOTIC ANALYSIS FOR A NONSTANDARD CAHN-HILLIARD SYSTEM WITH VISCOSITY

作者：Colli Pierluigi^*; Gilardi Gianni; Podio Guidugli Paolo; Sprekels Juergen

来源：Discrete and Continuous Dynamical Systems - Series S, 2013, 6(2): 353-368.

DOI：10.3934/dcdss.2013.6.353

• Viscous Cahn-Hilliard system
• phase field model
• asymptotic limit
• existence of solutions

This paper is concerned with a diffusion model of phase-field type, consisting of a parabolic system of two partial differential equations, interpreted as balances of microforces and microenergy, for two unknowns: the problem%26apos;s order parameter rho and the chemical potential mu; each equation includes a viscosity term respectively, epsilon partial derivative(t)mu and delta (t)rho with epsilon and delta two positive parameters; the field equations are complemented by Neumann homogeneous boundary conditions and suitable initial conditions. In a recent paper [5], we proved that this problem is well-posed and investigated the long-time behavior of its (epsilon, delta)-solutions. Here we discuss the asymptotic limit of the system as epsilon tends to 0. We prove convergence of (epsilon, delta)-solutions to the corresponding solutions for the case epsilon = 0, whose long-time behavior we characterize; in the proofs, we employ compactness and monotonicity arguments.

• 出版日期2013-4