On Maxwell's system with a thermal effect

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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

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

Abstract
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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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