• search hit 3 of 8
Back to Result List

An asymptotic analysis for a nonstandard Cahn-Hilliard system with viscosity

Please always quote using this URN:urn:nbn:de:0296-matheon-10676
  • 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's order parameter $\rho$} and the chemical potential $\mu$; each equation includes a viscosity term -- respectively, $\varepsilon \,\partial_t\mu$ and $\delta\,\partial_t\rho$ -- with $\varepsilon$ and $\delta$ two positive parameters; the field equations are complemented by Neumann homogeneous boundary conditions and suitable initial conditions. In a recent paper \cite{CGPS3}, we proved that this problem is \wepo\ and investigated the \loti\ \bhv\ of its $(\varepsilon,\delta)-$solutions. Here we discuss the asymptotic limit of the system as $\eps$ tends to $0$. We prove convergence of $(\varepsilon,\delta)-$solutions to the corresponding solutions for the case $\eps =0$, whose long-time behavior we characterize; in the proofs, we employ compactness and monotonicity arguments.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Pierluigi Colli, Gianni Gilardi, Paolo Podio-Guidugli, Jürgen Sprekels
URN:urn:nbn:de:0296-matheon-10676
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/02/17
Release Date:2012/02/17
Tag:asymptotic limit; existence of solutions; phase field model; viscous Cahn-Hilliard system
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K55 Nonlinear parabolic equations
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids / 74A15 Thermodynamics
Preprint Number:922
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.