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

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  • Anyin Xia
  • Mingshu Fan
  • Shan Li

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.

Suggested Citation

  • Anyin Xia & Mingshu Fan & Shan Li, 2013. "Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, August.
    • Handle: RePEc:hin:jnljam:387565
    DOI: 10.1155/2013/387565
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