Asymptotics of a solution of a nonlinear system of diffusion of a magnetic field into a substance

Siberian Mathematical Journal

Volumn 47, Issue 5, 2006, Pages 867-878

  Jangveladze, T A ^a   Kiguradze, Z V ^a  

^a TBILISI STATE UNIVERSITY   (Georgia)

Author keywords

Asymptotics; Diffusion of a magnetic field; Nonlinear integro differential system

Indexed keywords

EID: 33749188634     PISSN: 00374466     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11202-006-0095-5     Document Type: Article

References (19)

1. Landau L. D. and Lifshits E. M., Electrodynamics of Continuum Media [in Russian], Gostekhteorizdat, Moscow (1958).
2. Gordeziani D. G., Dzhangveladze T. A., and Korshiya T. K., "On existence and uniqueness of the solution of a certain class of nonlinear parabolic problems," Differentsial'nye Uravneniya, 19, No. 7, 1197-1207 (1983).
3. Gordeziani D. G., Dzhangveladze T. A., and Korshiya T. K., "On a class of nonlinear parabolic equations arising in problems of diffusion of an electromagnetic field," Trudy I. N. Vekua Inst. Prikl. Mat., 13, 7-35 (1983).
4. Dzhangveladze T. A., "The first boundary-value problem for a nonlinear equation of parabolic type," Dokl. Akad. Nauk SSSR, 269, No. 4, 839-842 (1983).
5. Vishik M. I., "On solvability of boundary-value problems for quasilinear parabolic equations of higher order," Mat. Sb., 59, No. 101, 289-325 (1962).
6. Lions J.-L., Some Methods for Solving Nonlinear Boundary Value Problems [Russian translation], Mir, Moscow (1972).
7. Dzhangveladze T. A., "On a nonlinear integro-differential equation of parabolic type," Differentsial'nye Uravneniya, 21, No. 1, 41-46 (1985).
8. Jangveladze T. A. and Kiguradze Z. V., "The asymptotic behavior of the solution of one nonlinear integro-differential parabolic equation," Rep. Enl. Sess. Sem. I. Vekua Inst. Appl. Math., 10, No. 1, 36-38 (1995).
9. Laptev G. I., "Quasilinear parabolic equations containing a Volterra operator in the coefficients," Mat. Sb., 136, No. 4, 530-540 (1988).
10. Laptev G. I., "Mathematical singularities of problems associated with the penetration of a magnetic field into a substance," Zh. Vychislit. Mat. i Mat. Fiziki, 28, No. 9, 1332-1345 (1988).
11. Laptev G. I., "Mathematical singularities of problems associated with the penetration of a magnetic field into a substance for quasistationary approximation," Izv. Vyssh. Uchebn. Zaved. Mat., No. 7, 10-12 (1989).
12. Dzhangveladze T. A., Lyubimov B. Ya., and Korshiya T. K., "Numerical solution of a class of nonisothermal diffusion problems of an electromagnetic field," Trudy I. N. Vekua Inst. Prikl. Mat., 18, 5-47 (1986).
13. Long N. T. and Dinh A. P. N., "Nonlinear parabolic problem associated with the penetration of a magnetic field into a substance," Math. Methods Appl. Sci., 16, No. 4, 281-295 (1993).
14. Jangveladze T. A., "On one class of nonlinear integro-differential parabolic equations," Rep. Sem. I. Vekua Inst. Appl. Math., 23, 51-87 (1997).
15. Jangveladze T. A. and Kiguradze Z. V., "Estimates of a stabilization rate as t → ∞ of solutions of a nonlinear integro-differential equation," Georgian Math. J., 9, No. 1, 57-70 (2002).
16. Jangveladze T. A. and Kiguradze Z. V., "Estimates of a stabilization rate as t → ∞ of solutions of a nonlinear integro-differential diffusion system," J. Appl. Math. Inform. Mech., 8, No. 2, 1-19 (2003).
17. Kiguradze Z. V., "The asymptotic behavior of the solutions of one nonlinear integro-differential model," Sem. of I. Vekua Inst. of Appl. Math., REPORTS, 30, 21-31 (2004).
18. Kazhikhov A. V., "On stabilization of solutions to a boundary-value problem for equations of a barotropic viscous fluid with one space variable," Differentsial'nye Uravneniya, 15, No. 4, 662-667 (1979).
19. Antontsev S. N., Kazhikhov A. V., and Monakhov V. N., Boundary Value Problems of Inhomogeneous Fluid Mechanics [in Russian], Nauka, Novosibirsk (1983).