Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity
The asymptotic behavior of the solution for the Dirichlet problem of the parabolic equation with nonlocal term ut=urr+ur/r+f(u)/(a+2πb∫01f(u)rdr)2, for 0<r<1, t>0,u1,t=u′(0,t)=0, for t>0, ur,0=u0r, for 0≤r≤1. The model prescribes the dimensionless temperature when the electric cur...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/387565 |
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| _version_ | 1832563905831895040 |
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| author | Anyin Xia Mingshu Fan Shan Li |
| author_facet | Anyin Xia Mingshu Fan Shan Li |
| author_sort | Anyin Xia |
| collection | DOAJ |
| description | The asymptotic behavior of the solution for the Dirichlet problem of the parabolic equation with nonlocal term ut=urr+ur/r+f(u)/(a+2πb∫01f(u)rdr)2, for 0<r<1, t>0,u1,t=u′(0,t)=0, for t>0, ur,0=u0r, for 0≤r≤1. 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. |
| format | Article |
| id | doaj-art-4bb25dc130a84ed587fd1a022c9d5810 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4bb25dc130a84ed587fd1a022c9d58102025-02-03T01:12:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/387565387565Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal ElectricityAnyin Xia0Mingshu Fan1Shan Li2School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, ChinaDepartment of Mathematics, Jincheng College of Sichuan University, Chengdu 611731, ChinaBusiness School, Sichuan University, Chengdu 610064, ChinaThe asymptotic behavior of the solution for the Dirichlet problem of the parabolic equation with nonlocal term ut=urr+ur/r+f(u)/(a+2πb∫01f(u)rdr)2, for 0<r<1, t>0,u1,t=u′(0,t)=0, for t>0, ur,0=u0r, for 0≤r≤1. 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.http://dx.doi.org/10.1155/2013/387565 |
| spellingShingle | Anyin Xia Mingshu Fan Shan Li Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity Journal of Applied Mathematics |
| title | Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity |
| title_full | Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity |
| title_fullStr | Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity |
| title_full_unstemmed | Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity |
| title_short | Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity |
| title_sort | asymptotic stability for an axis symmetric ohmic heating model in thermal electricity |
| url | http://dx.doi.org/10.1155/2013/387565 |
| work_keys_str_mv | AT anyinxia asymptoticstabilityforanaxissymmetricohmicheatingmodelinthermalelectricity AT mingshufan asymptoticstabilityforanaxissymmetricohmicheatingmodelinthermalelectricity AT shanli asymptoticstabilityforanaxissymmetricohmicheatingmodelinthermalelectricity |