Asymptotic behavior of solutions of a two-phase problem of microwave heating in the one-dimensional case

被引：0
作者：
V. Reitmann
N. Yu. Yumaguzin
机构：
[1] St. Petersburg State University, St. Petersburg 199034
来源：
Vestnik St. Petersburg University: Mathematics | 2012年 / 45卷 / 3期
关键词：
asymptotic behavior; parabolic-hyperbolic system; weak solution;
D O I：
10.3103/S1063454112030053
中图分类号：
学科分类号：
摘要：
The present paper is concerned with the asymptotic behavior of the system describing the material heating due to microwave radiation in the one-dimensional case. The material is assumed to have inhomogeneous structure and two-phase properties. The parabolic-hyperbolic system describing the heat in the one-dimensional case is studied. The results on the asymptotic behavior of weak solutions of the systems are obtained. © 2012 Allerton Press, Inc.
引用
收藏
页码：141 / 144
页数：3
相关论文
共 10 条
[1]  
Morgan J., Yin H.-M., On Maxwell's System with a Thermal Effect, Discrete and Cont. Dyn. Sys. Ser. B., 1, pp. 485-494, (2001)
[2]  
Kalinin Y.N., Reitmann V., Yumaguzin N.Y., Asymptotic Behavior of Maxwell's Equation in One-Space Dimension with Thermal Effect, Discrete and Cont. Dyn. Sys. Suppl. 2011, 2, pp. 754-762, (2011)
[3]  
Reitmann V., Yumaguzin N.Y., Stability Analysis for Maxwell's Equation with a Thermal Effect in One Space Dimension, J. Math. Sci.
[4]  
Manoranjan V.S., Showalter R., Yin H.-M., On Two-Phase Stefan Problem Arising from a Microwave Heating Process, Discrete and Cont. Dyn. Sys. Ser. A, 4, 15, pp. 1155-1168, (2006)
[5]  
Serkova N.D., Two-Phase Heating Problem of Inhomogeneous Material, (2011)
[6]  
Kamenomostskaya S.L., On Stefan's Problem, Mat. Sb. (N.S.), 53, 4, pp. 489-514, (1961)
[7]  
Ishii H., Asymptotic Stability and Existence of Almost-Periodic Solutions for the One-Dimensional, Two-Phase Stefan Problem, Math. Japonica, 25, pp. 379-393, (1980)
[8]  
Niezgodka M., Pawlow I., A Generalized Stefan Problem in Several Space Variables, Appl. Math. Optim., 9, pp. 193-224, (1983)
[9]  
Yin H.-M., On Maxwell's Equations in an Electromagnetic Field with the Temperature Effect, SIAM J. Math. Anal., 29, pp. 637-651, (1998)
[10]  
Ladyzhenskaya O.A., Solonnikov V.A., Ural'tseva N.N., Linear and Quasi-Linear Equations of Parabolic Type, (1967)
1