# Regularity of weak solution to Maxwell's equations and applications to microwave heating

@article{Yin2004RegularityOW,
title={Regularity of weak solution to Maxwell's equations and applications to microwave heating},
author={Hong Ming Yin},
journal={Journal of Differential Equations},
year={2004},
volume={200},
pages={137-161}
}
• H. Yin
• Published 1 June 2004
• Mathematics
• Journal of Differential Equations
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## References

SHOWING 1-10 OF 24 REFERENCES
On Maxwell's Equations with a Temperature Effect, II
• Mathematics
• 1998
Abstract:In this paper we study Maxwell's equations with a thermal effect. This system models an induction heating process where the electric conductivity σ strongly depends on the temperature $u$.
On the solution of time-harmonic scattering problems for Maxwell's equations
• Mathematics
• 1996
This paper deals with the scattering of a monochromatic electromagnetic wave by a perfect conductor surrounded by a locally inhomogeneous medium. The direct numerical solution of this problem by a
Regularity of weak solutions of Maxwell's equations with mixed boundary-conditions
In this paper global Hs- and Lp-regularity results for the stationary and transient Maxwell equations with mixed boundary conditions in a bounded spatial domain are proved. First it is shown that
ON MAXWELL'S EQUATIONS IN AN ELECTROMAGNETIC FIELD WITH THE TEMPERATURE EFFECT
This paper deals with Maxwell's equations coupled with a nonlinear heat equation. The system models an induction heating process for a conductive material in which the electrical conductivity
Optimal regularity of solution to a degenerate elliptic system arising in electromagnetic fields
In this paper we prove a fundamental estimate for the weak solution of a degenerate elliptic system: $\nabla\times [\rho(x)\nabla\times H]=F$, $\nabla\cdot H=0$ in a bounded domain in $R^3$,
Microwave Heating of Dispersive Media
The heating of a compact dispersive target by a pulsed, plane microwave is modeled and studied herein, and a new theory from which a considerable amount of information can be deduced.
On the Hölder Continuity of Solutions of a Certain System Related to Maxwell's Equations
• Mathematics
SIAM J. Math. Anal.
• 2002
The Holder continuity of weak solutions of the Maxwell's equations in a quasi-stationary electromagnetic field is proved and the Cα regularity of weak problems in this system is proved.
The Cauchy Problem in Kinetic Theory
Preface 1. Properties of the Collision Operator. Kinetic Theory, Derivation of the Equations, The Form of the Collision Operator, The Hard Sphere Case, Conservation Laws and the Entropy, Relevance of
Hot spot formation in microwave heated ceramic fibres
An analysis of microwave heating of a thin ceramic cylinder in a single mode, highly resonant cavity is presented. Realistic assumptions regarding the effective electrical conductivity, thermal