On Maxwell's system with a thermal effect

J. J. Morgan; Hong-Ming Yin

doi:10.3934/dcdsb.2001.1.485

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2001, Volume 1, Issue 4: 485-494. Doi: 10.3934/dcdsb.2001.1.485

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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
2.
Department of Pure and Applied Mathematics, Washington State University, Pullman, WA 9916

Received: January 31, 2001

Revised: June 30, 2001

Published: October 2001

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Abstract

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.

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Mathematics Subject Classification: 35B45, 35B60, 35L20, 35K20, 35K15, 35Q99, 80A20.

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