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.
Citation
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. https://doi.org/10.1155/2013/387565