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Article Contents

# On Maxwell's system with a thermal effect

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

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