American Institute of Mathematical Sciences

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November  2001, 1(4): 485-494. doi: 10.3934/dcdsb.2001.1.485

On Maxwell's system with a thermal effect

J. J. Morgan 1, and  Hong-Ming Yin 2,

1. 

Department of Mathematics, Texas A & M University, College Station, Texas, 77843-3368, United States
2. 

Department of Pure and Applied Mathematics, Washington State University, Pullman, WA 9916, United States

Received  February 2001 Revised  July 2001 Published  September 2001

In this paper we study Maxwell’s system coupled with a heat equation in one space dimension. The system models a microwave heating process. The feature of the model is that the electric conductivity $\sigma(u)$ strongly depends on the temperature. It is shown that the system has a global solution for $\sigma(u)=1+u^k$ with any $k\ge 1$. The long time behavior of the solution is also investigated.
Keywords: global existence., Maxwell’s System, electric conductivity, microwave heating, thermal effects, partial differential equations.
Mathematics Subject Classification: 35B45, 35B60, 35L20, 35K20, 35K15, 35Q99, 80A2.
Citation: J. J. Morgan, Hong-Ming Yin. On Maxwell's system with a thermal effect. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 485-494. doi: 10.3934/dcdsb.2001.1.485
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