On Maxwell's equations in an electromagnetic field with the temperature effect

SIAM Journal on Mathematical Analysis

Volumn 29, Issue 3, 1998, Pages 637-651

  Yin, Hong Ming ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

Macrowave heating; Maxwell's system with thermal effect

Indexed keywords

EID: 0032391614     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141097316159     Document Type: Article

References (20)

1. S. N. ANTONTSEV AND M. CHIPOT, The thermistor problem: Existence, smoothness, uniqueness, blowup. SIAM J. Math. Anal., 25 (1994), pp. 1128-1156.
2. L. BOCCARDO AND T. GALLOUET, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal., 87 (1989), pp. 149-169.
3. A. BOSSAVIT, Free boundaries in induction heating, Control Cybernet., 14 (1985), pp. 69-96.
4. C. J. COLEMAN, On the microwave hot spot problem, J. Austral. Math. Soc. Ser. B., 33 (1991), pp. 1-8.
5. E. J. DAVIES, Conduction and Induction Heating, Per Peregrimus Ltd., London, 1990.
6. R. DIPERNA AND P. L. LIONS, Global weak solutions of Vlasov-Maxwell system, Comm. Pure Appl. Math., 42 (1989), pp. 729-757.
7. R. GLASSEY, The Cauchy Problem in Kinetic Theory, SIAM, Philadelphia, PA, 1996.
8. J. M. HILL AND A. H. PINCOMBE, Some similarity temperature profiles for the microwave heating of a half-space, J. Austral. Math. Ser. B., 33 (1992), pp. 290-320.
9. G. A. KRIEGSMANN, Microwave heating of dispersive media, SIAM J. Appl. Math., 53 (1993), pp. 655-669.
10. G. A. KRIEGSMANN, Hot Spot Formation in Microwave Heated Ceramic. Fibers, CAMS Research Report 96-17, New Jersey Institute of Technology, 1996.
11. L. D. LANDAU AND E. M. LIFSHITZ, Electrodynamics of Continuous Media, Pergarnon Press, New York, 1960.
12. O. A. LADYZENSKAJA, V. A. SOLONNIKOV, AND N. N. URAL'CEVA, Linear and Quasi-linear Equations of Parabolic Type, Transl. Math. Monogr. 23, Amer. Math. Soc., Providence, RI, 1968.
13. A. LORENZI, Direct and inverse integrodifferential Maxwell's problems for dispersive media related to cylindrical domains, in Inverse Problems in Diffusion Processes, H. W. Engl and W. Rundell, eds., SIAM, Philadelphia, PA, 1995.
14. A. C. METAXAS AND R. J. MEREDITH, Industrial Microwave Heating, IEE Power Engineering Series, Vol. 4. Per Peregrimus Ltd., London, 1983.
15. p(0, T; B), Ann. Mat. Pure Appl., 146 (1987), pp. 65-96.
16. N. F. SMYTH, Microwave heating of bodies with temperature dependent properties, Wave Motion, 12 (1990), pp. 171-186.
17. J. SMOLLER, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1982.
18. H. F. WEIBERGER, A first course in Partial Differential Equations, Blaisdell Publishing Company, Waltham, MA, 1965.
19. H. M. YIN, Global solutions of Maxwell's equations in an electromagnetic field with the temperature - dependent electrical conductivity, European J. Appl. Math., 5 (1994), pp. 57-64.
20. H. M. YIN, Regularity of Solutions to Maxwell's System in Quasi-Stationary Electromagnetic Fields and Applications, Comm. Partial Differential Equations, 22 (1997), pp. 1029-1053.