Premium
Global regular solutions to Cahn–Hilliard system coupled with viscoelasticity
Author(s) -
Pawłow Irena,
Zaja̧czkowski Wojciech M.
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1131
Subject(s) - uniqueness , viscoelasticity , mathematics , cahn–hilliard equation , interval (graph theory) , type (biology) , set (abstract data type) , property (philosophy) , mathematical analysis , thermodynamics , partial differential equation , computer science , physics , combinatorics , ecology , philosophy , epistemology , biology , programming language
In this paper we prove the existence and uniqueness of a global in time, regular solution to the Cahn–Hilliard system coupled with viscoelasticity. The system arises as a model, regularized by a viscous damping, of phase separation process in a binary deformable alloy quenched below a critical temperature. The key tools in the analysis are estimates of absorbing type with the property of exponentially time‐decreasing contribution of the initial data. Such estimates allow not only to prolong the solution step by step on the infinite time interval but also to conclude the existence of an absorbing set. Copyright © 2009 John Wiley & Sons, Ltd.