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Journal of Applied MathematicsVolume 2013 2013, Article ID 387565, 5 pages

Research Article

School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China

Department of Mathematics, Jincheng College of Sichuan University, Chengdu 611731, China

Business School, Sichuan University, Chengdu 610064, China

Received 12 June 2013; Accepted 4 July 2013

Academic Editor: Alain Miranville

Copyright © 2013 Anyin Xia et al. 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.


The asymptotic behavior of the solution for the Dirichlet problem of the parabolic equation with nonlocal term , , . The model prescribes the dimensionless temperature when the electric current flows through two conductors, subject to a fixed potential difference. One of the electrical resistivity of the axis-symmetric conductor depends on the temperature and the other one remains constant. The main results show that the temperature remains uniformly bounded for the generally decreasing function , and the global solution of the problem converges asymptotically to the unique equilibrium.

Author: Anyin Xia, Mingshu Fan, and Shan Li



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