Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction

Annalisa Iuorio; Stefano Melchionna

doi:10.3934/dcds.2018163

Article Contents

2018, Volume 38, Issue 8: 3765-3788. Doi: 10.3934/dcds.2018163

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Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction

Annalisa Iuorio^1, , and
Stefano Melchionna^2,

1.
Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria
2.
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

* Corresponding author: Annalisa Iuorio
* Corresponding author: Annalisa Iuorio

Received: June 30, 2017

Revised: December 31, 2017

Published: May 2018

The authors would like to acknowledge the Austrian Science Fund (FWF) for financial support (AI through project W1245, SM through project P27052-N25)

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Abstract

In this paper we study the long-time behavior of a nonlocal Cahn-Hilliard system with singular potential, degenerate mobility, and a reaction term. In particular, we prove the existence of a global attractor with finite fractal dimension, the existence of an exponential attractor, and convergence to equilibria for two physically relevant classes of reaction terms.

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Mathematics Subject Classification: Primary: 37L30; Secondary: 45K05.

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Figure 1. Illustration of $r_\kappa$ for a reaction term $g$ satisfying (A1), (A2).

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