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} }
44 Citations
The coupled heat Maxwell equations with temperature-dependent permittivity
- Mathematics, Physics
- 2021
Regularity of weak solution for a coupled system arising from a microwave heating model
- MathematicsEuropean Journal of Applied Mathematics
- 2013
In this paper, we study the regularity of a weak solution for a coupled system derived from a microwave-heating model. The main feature of this model is that electric conductivity in the…
Existence and regularity of a weak solution to Maxwell's equations with a thermal effect
- Mathematics
- 2006
This paper deals with Maxwell's equations with a thermal effect, where the electric conductivity strongly depends on the temperature. It is shown that the coupled system has a global weak solution…
The Regularity of Solution for Weakly Coupled System Derived by Microwave Heating Model
- MathematicsMathematics
- 2019
In this paper, we study the regularity of the weak solution of the coupled system derived from the microwave heating model with frequency variable. We first show that the weak solution E of the…
On local constraints and regularity of PDE in electromagnetics. Applications to hybrid imaging inverse problems
- Mathematics
- 2014
The first contribution of this thesis is a new regularity theorem for time harmonic Maxwell’s equations with less than Lipschitz complex anisotropic coefficients. By using the $L^p$ theory for…
A nonlocal formulation for the problem of microwave heating of material with temperature dependent conductivity
- Mathematics
- 2021
Abstract. Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell’s equations coupled with the heat equation. The thermal…
W1,p Regularity of Weak Solutions to Maxwell’s Equations
- Mathematics
- 2020
In this paper, we study the steady-state Maxwell’s equations. The weak solution defined in weak formulation is considered, and the global existence is obtained in general bounded open domain. The…
Elliptic Regularity Theory Applied to Time Harmonic Anisotropic Maxwell's Equations with Less than Lipschitz Complex Coefficients
- MathematicsSIAM J. Math. Anal.
- 2014
Using regularity theory for second order elliptic partial differential equations, W^{1,p} estimates and Holder estimates for electric and magnetic fields up to the boundary are derived, together with their higher regularity counterparts.
Fully discrete T‐ψ finite element method to solve a nonlinear induction hardening problem
- MathematicsNumerical Methods for Partial Differential Equations
- 2020
We study an induction hardening model described by Maxwell's equations coupled with a heat equation. The magnetic induction field is assumed a nonlinear constitutional relation and the electric…
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
- Mathematics
- 1999
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
- Mathematics
- 1998
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
- Mathematics
- 2001
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
- PhysicsSIAM J. Appl. Math.
- 1993
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
- MathematicsSIAM 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
- Mathematics
- 1987
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
- Physics
- 1997
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…