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@article{CMFD_2012_46_a6, author = {V. Reitmann and N. Yumaguzin}, title = {Stability analysis for {Maxwell's} equation with a~thermal effect in one space dimension}, journal = {Contemporary Mathematics. Fundamental Directions}, pages = {129--140}, publisher = {mathdoc}, volume = {46}, year = {2012}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/CMFD_2012_46_a6/} }
TY - JOUR AU - V. Reitmann AU - N. Yumaguzin TI - Stability analysis for Maxwell's equation with a~thermal effect in one space dimension JO - Contemporary Mathematics. Fundamental Directions PY - 2012 SP - 129 EP - 140 VL - 46 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CMFD_2012_46_a6/ LA - ru ID - CMFD_2012_46_a6 ER -
%0 Journal Article %A V. Reitmann %A N. Yumaguzin %T Stability analysis for Maxwell's equation with a~thermal effect in one space dimension %J Contemporary Mathematics. Fundamental Directions %D 2012 %P 129-140 %V 46 %I mathdoc %U http://geodesic.mathdoc.fr/item/CMFD_2012_46_a6/ %G ru %F CMFD_2012_46_a6
V. Reitmann; N. Yumaguzin. Stability analysis for Maxwell's equation with a~thermal effect in one space dimension. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 2, Tome 46 (2012), pp. 129-140. http://geodesic.mathdoc.fr/item/CMFD_2012_46_a6/
[1] Kamenomostskaya S. L., “O zadache Stefana”, Matem. sb., 53(95):4 (1961), 489–514 | MR | Zbl
[2] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967 | MR
[3] Oleinik O. A., “Ob odnom metode resheniya obschei zadachi Stefana”, Dokl. AN SSSR, 135 (1960), 1054–1057 | MR
[4] Serkova N., Dvukhfazovaya zadacha teploperedachi dlya neodnorodnogo materiala., Diplomnaya rabota, Sankt-Peterburgskii gosudarstvennyi universitet, 2011
[5] Cannon J. R., DiBenedetto E., “On the existence of weak solutions to an $n$-dimensional Stefan problem with nonlinear bondary conditions”, SIAM J. Math. Anal., 11:4 (1978), 632–645 | DOI | MR
[6] Deuflhard P., Weiser M., Seebass M., “A new nonlinear elliptic multilevel FEM applied to regional hyperthermia”, Comput. Vis. Sci., 3:3 (2000), 115–120 | DOI | Zbl
[7] Dewynne J. N., Howison S. D., Ockendon J. R., Xie W., “Asymptotic behaviour of solutions to the Stefan problem with a kinetic condition at the free boundary”, J. Aust. Math. Soc., 31 (1989), 81–96 | DOI | MR | Zbl
[8] Ermakov I., Kalinin Y., Reitmann V., “Determining modes and almost periodic integrals for cocycles”, Differential Equations and Control Processes, 4 (2011), 113–137 | MR
[9] Friedman A., “The Stefan problem in several space variables”, Trans. Amer. Math. Soc., 132 (1968), 57–87 | MR
[10] Kalinin Y., Reitmann V., Yumaguzin N., “Asymptotic behavior of Maxwell's equation in one-space dimension with termal effect”, Discrete Contin. Dyn. Syst., 2011, Suppl., Vol. 2, 754–762 | MR
[11] Kumar S., Katiyar V. K., “Numerical study on phase change heat transfer during combined hyperthermia and cryosurgical treatment of lung cancer”, Int. J. of Appl. Math. and Mech. (e-Journal System), 3:3 (2007), 1–17
[12] Manoranjan V. S., Showalter R., Yin H.-M., “On two-phase Stefan problem arising from a microwave heating process”, Discrete Contin. Dyn. Syst., 15:4 (2006), 1155–1168 | DOI | MR | Zbl
[13] Morgan J., Yin H.-M., “On Maxwell's system with a thermal effect”, Discrete Contin. Dyn. Syst. Ser. B, 1 (2001), 485–494 | DOI | MR | Zbl
[14] Niezgodka M., Pawlow I., “A generalized Stefan problem in several space variables”, Appl. Math. Optim., 9 (1983), 193–224 | DOI | MR | Zbl
[15] Yin H.-M., “Regularity of weak solution to Maxwell's equations and applications to microwave heating”, J. Differential Equations, 200 (2004), 137–161 | DOI | MR | Zbl