Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity

Anyin Xia, Mingshu Fan and Shan Li

Journal of Applied Mathematics, 2013, vol. 2013, 1-5

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:387565

DOI: 10.1155/2013/387565

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