## Topological Methods in Nonlinear Analysis

### Weak solutions to 3-D Cahn-Hilliard system in elastic solids

#### Abstract

In this paper we prove the existence and some time regularity of weak solutions to a three-dimensional (3-D) Cahn-Hilliard system coupled with nonstationary elasticity. Such nonlinear parabolic-hyperbolic system arises as a model of phase separation in deformable alloys. The regularity result is based on the analysis of time differentiated problem by means of the Faedo-Galerkin method. The obtained regularity provides a first step to the proof of strong solvability of the problem to be presented in a forthcoming paper [I. Pawłow, W. M. Zajączkowski, Strong solvability of 3-D Cahn–Hilliard system in elastic solids, Math. Methods Appl. Sci.].

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 32, Number 2 (2008), 347-377.

Dates
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463151170

Mathematical Reviews number (MathSciNet)
MR2494061

Zentralblatt MATH identifier
1179.35093

#### Citation

Pawłow, Irena; Zajączkowski, Wojciech M. Weak solutions to 3-D Cahn-Hilliard system in elastic solids. Topol. Methods Nonlinear Anal. 32 (2008), no. 2, 347--377. https://projecteuclid.org/euclid.tmna/1463151170

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