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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 910406, 18 pages
http://dx.doi.org/10.1155/2012/910406
Research Article

The Systems of Nonlinear Gradient Flows on Metric Spaces and Its Gamma-Convergence

Department of Mathematics, Fu Jen Catholic University, New Taipei City 24205, Taiwan

Received 2 July 2012; Accepted 2 September 2012

Academic Editor: Norimichi Hirano

Copyright © 2012 Mao-Sheng Chang and Bo-Cheng Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We first establish the explicit structure of nonlinear gradient flow systems on metric spaces and then develop Gamma-convergence of the systems of nonlinear gradient flows, which is a scheme meant to ensure that if a family of energy functionals of several variables depending on a parameter Gamma-converges, then the solutions to the associated systems of gradient flows converge as well. This scheme is a nonlinear system edition of the notion initiated by Sylvia Serfaty in 2011.