On a nonlocal viscous phase separation model.
Preprintreihe der Fakultät Mathematik 23/201,
A nonlocal viscous model of phase separation is presented. It is derived from a
minimization of free energy containing a nonlocal part due to particle interaction.
In contrast to the classical Cahn-Hilliard theory with higher order terms this leads
to an evolution system of second order parabolic equations for the particle densities,
coupled by nonlocal drift and viscosity terms, which allow reasonable bounds for the
concentrations. Applying fixed-point arguments and compactness results we prove
the existence of variational solutions in standard Hilbert spaces for evolution systems.
Using the free energy as Lyapunov functional the asymptotic state of the system is
investigated and characterized by a variational principle.
|Item Type:||Monograph (Working Paper)|
|Institutions:|| Mathematics > Prof. Dr. Harald Garcke|
|Keywords:||Nonlocal phase separation models; viscous phase separation models, Cahn-
Hilliard equation; Integrodifferential equations ; Initial value problems; Nonlinear evolution
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||07 Sep 2011 06:10|
|Last Modified:||07 Sep 2011 06:10|