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2013 Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity
Anyin Xia, Mingshu Fan, Shan Li
J. Appl. Math. 2013: 1-5 (2013). DOI: 10.1155/2013/387565


The asymptotic behavior of the solution for the Dirichlet problem of the parabolic equation with nonlocal term ut=urr+ur/r+f(u)/(a+2πb01f(u)rdr)2, for 0<r<1, t>0,u1,t=u(0,t)=0, for t>0, ur,0=u0r, for 0r1. 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 f(s), and the global solution of the problem converges asymptotically to the unique equilibrium.


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Anyin Xia. Mingshu Fan. Shan Li. "Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity." J. Appl. Math. 2013 1 - 5, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950645
MathSciNet: MR3090624
Digital Object Identifier: 10.1155/2013/387565

Rights: Copyright © 2013 Hindawi


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