Large time behavior of the solution to an initial-boundary value problem with mixed boundary conditions for a nonlinear integro-differential equation

• Autorzy: Temur Jangveladze , Zurab Kiguradze
• Języki publikacji: EN

Abstrakty

EN

Large time behavior of the solution to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. Furthermore, the rate of convergence is given. Initial-boundary value problem with mixed boundary conditions is considered.

Słowa kluczowe

EN

Nonlinear integro-differential equation; Large time behavior

Kategorie tematyczne

• 74H40: Long-time behavior of solutions
• 45K05: Integro-partial differential equations
• 35K55: Nonlinear parabolic equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 866-873

Daty

wydano

2011-08-01

online

2011-05-26

Twórcy

autor

Temur Jangveladze

autor

Zurab Kiguradze

• Ivane Javakhishvili Tbilisi State University

Bibliografia

• [1] Aptsiauri M., Jangveladze T., Kiguradze Z., Large time behavior of solutions and numerical approximation of nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance, J. Appl. Math. Inform. Mech., 2008, 13(2), 3–17
• [2] Aptsiauri M., Jangveladze T., Kiguradze Z., On asymptotic behavior of solution of one nonlinear one-dimensional integro-differential analogue of Maxwell’s system, Rep. Enlarged Sess. Semin. I. Vekua Appl. Math., 2009, 23, 3–6
• [3] Bai Y., Backward solutions to nonlinear integro-differential systems, Cent. Eur. J. Math., 2010, 8(4), 807–815 http://dx.doi.org/10.2478/s11533-010-0042-3
• [4] Bai Y., Zhang P., On a class of Volterra nonlinear equations of parabolic type, Appl. Math. Comput., 2010, 216(1), 236–240 http://dx.doi.org/10.1016/j.amc.2010.01.044
• [5] Dzhangveladze T.A., Investigation of the First Boundary Value Problem for Some Nonlinear Integro-Differential Equations of Parabolic Type, Tbilisi State University, Tbilisi, 1983 (in Russian)
• [6] Dzhangveladze T.A., The first boundary value problem for a nonlinear equation of parabolic type, Dokl. Akad. Nauk SSSR, 1983, 269(4), 839–842 (in Russian)
• [7] Dzhangveladze T.A., A nonlinear integro-differential equation of parabolic type, Differ. Uravn., 1985, 21(1), 41–46 (in Russian)
• [8] Dzhangveladze T.A., Kiguradze Z.V., On the stabilization of solutions of an initial-boundary value problem for a nonlinear integro-differential equation, Differ. Uravn., 2007, 43(6), 833–840 (in Russian)
• [9] Dzhangveladze T.A., Lyubimov B.Ya., Korshiya T.K., On the numerical solution of a class of nonisothermic problems of the diffusion of an electromagnetic field, Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy, 1986, 18, 5–47 (in Russian)
• [10] Gordeziani D.G., Dzhangveladze T.A., Korshiya T.K., Existence and uniqueness of the solution of a class of nonlinear parabolic problems, Differ. Uravn., 1983, 19(7), 1197–1207 (in Russian)
• [11] Gripenberg G., Londen S.-O., Staffans O., Volterra Integral and Functional Equations, Encyclopedia Math. Appl., 34, Cambridge University Press, Cambridge, 1990 http://dx.doi.org/10.1017/CBO9780511662805
• [12] Jangveladze T.A., On one class of nonlinear integro-differential parabolic equations, Semin. I. Vekua Inst. Appl. Math. Rep., 1997, 23, 51–87
• [13] Jangveladze T., Kiguradze Z., The asymptotic behavior of the solutions of one nonlinear integro-differential parabolic equation, Rep. Enlarged Sess. Semin. I. Vekua Appl. Math., 1995, 10(1), 36–38
• [14] Jangveladze T.A., Kiguradze Z.V., Asymptotics of a solution of a nonlinear system of diffusion of a magnetic field into a substance, Sibirsk. Mat. Zh., 2006, 47(5), 1058–1070 (in Russian)
• [15] Jangveladze T., Kiguradze Z., Asymptotics of solution and finite difference scheme to a nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance, WSEAS Trans. Math., 2009, 8(8), 467–477
• [16] Jangveladze T., Kiguradze Z., Neta B., Finite difference approximation of a nonlinear integro-differential system, Appl. Math. Comput., 2009, 215(2), 615–628 http://dx.doi.org/10.1016/j.amc.2009.05.061
• [17] Jangveladze T., Kiguradze Z., Neta B., Large time asymptotic and numerical solution of a nonlinear diffusion model with memory, Comput. Math. Appl., 2010, 59(1), 254–273 http://dx.doi.org/10.1016/j.camwa.2009.07.052
• [18] Kiguradze Z., Finite difference scheme for a nonlinear integro-differential system, Proc. I. Vekua Inst. Appl. Math., 2000–2001, 50–51, 65–72
• [19] Kiguradze Z., The asymptotic behavior of the solutions of one nonlinear integro-differential model, Semin. I. Vekua Inst. Appl. Math. Rep., 2004, 30, 21–32
• [20] Ladyzhenskaya O.A., New equations for the description of the motions of viscous incompressible fluids, and global solvability for their boundary value problems, Trudy Mat. Inst. Steklov., 1967, 102, 85–104 (in Russian)
• [21] Lakshmikantham V., Rana Mohana Rao M., Theory of Integro-Differential Equations, Stability Control Theory Methods Appl., 1, Gordon and Breach, Lausanne, 1995
• [22] Landau L.D., Lifshitz E.M., Electrodynamics of Continuous Media, Course of Theoretical Physics, 8, Pergamon Press, Oxford-London-New York-Paris, 1960
• [23] Laptev G.I., Quasilinear parabolic equations that have a Volterra operator in the coefficients, Mat. Sb., 1988, 136(178)(4), 530–545 (in Russian)
• [24] Laptev G.I., Mathematical singularities of a problem on the penetration of a magnetic field into a substance, Zh. Vychisl. Mat. i Mat. Fiz., 1988, 28(9), 1332–1345 (in Russian)
• [25] Lin Y., Yin H.-M., Nonlinear parabolic equations with nonlinear functionals. J. Math. Anal. Appl., 1992, 168(1), 28–41 http://dx.doi.org/10.1016/0022-247X(92)90187-I
• [26] Lions J.-L., Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Gauthier-Villars, Paris, 1969
• [27] Long N.T., Dinh A.P.N., Nonlinear parabolic problem associated with the penetration of a magnetic field into a substance, Math. Methods Appl. Sci., 1993, 16(4), 281–295 http://dx.doi.org/10.1002/mma.1670160404
• [28] Vishik M., Solubility of boundary-value problems for quasi-linear parabolic equations of higher orders, Mat. Sb., 1962, 59(101) suppl., 289–325 (in Russian)

Identyfikatory

DOI

10.2478/s11533-011-0036-9