Аннотация:
Исследовано асимптотическое поведение решения при бесконечном возрастании времени системы нелинейных интегродифференциальных уравнений, возникающей при математическом моделировании задачи диффузии магнитного поля в вещество. Установлен соответствующий порядок сходимости.
Образец цитирования:
Т. А. Джангвеладзе, З. В. Кигурадзе, “Асимптотика решения нелинейной системы диффузии магнитного поля в вещество”, Сиб. матем. журн., 47:5 (2006), 1058–1070; Siberian Math. J., 47:5 (2006), 867–878
Temur Jangveladze, Zurab Kiguradze, Maia Kratsashvili, Beny Neta, “Numerical solution for a nonlinear diffusion model with source terms”, Georgian Mathematical Journal, 30:4 (2023), 539
Temur Jangveladze, Zurab Kiguradze, Springer Proceedings in Mathematics & Statistics, 276, Mathematics, Informatics, and Their Applications in Natural Sciences and Engineering, 2019, 117
Hecht F., Jangveladze T., Kiguradze Z., Pironneau O., “Finite Difference Scheme For One System of Nonlinear Partial Integro-Differential Equations”, Appl. Math. Comput., 328 (2018), 287–300
Sharma N., Khebchareon M., Sharma K., Pani A.K., “Finite Element Galerkin Approximations to a Class of Nonlinear and Nonlocal Parabolic Problems”, Numer. Meth. Part Differ. Equ., 32:4 (2016), 1232–1264
Liao H.-l., Zhao Y., “Linearly Localized Difference Schemes For the Nonlinear Maxwell Model of a Magnetic Field Into a Substance”, Appl. Math. Comput., 233 (2014), 608–622
Sharma N., Sharma K.K., “Unconditionally Stable Numerical Method For a Nonlinear Partial Integro-Differential Equation”, Comput. Math. Appl., 67:1 (2014), 62–76
Temur Jangveladze, Zurab Kiguradze, Beny Neta, Simeon Reich, “Finite element approximations of a nonlinear diffusion model with memory”, Numer Algor, 64:1 (2013), 127
Jangveladze T., Kiguradze Z., “Large time behavior of the solution to an initial-boundary value problem with mixed boundary conditions for a nonlinear integro-differential equation”, Cent Eur J Math, 9:4 (2011), 866–873
Jangveladze T., Kiguradze Z., Neta B., “Galerkin finite element method for one nonlinear integro-differential model”, Applied Mathematics and Computation, 217:16 (2011), 6883–6892
Bai Yuzhen, Zhang Pingping, “On a class of Volterra nonlinear equations of parabolic type”, Appl. Math. Comput., 216:1 (2010), 236–240
Jangveladze T., Kiguradze Z., Neta B., “Large time asymptotic and numerical solution of a nonlinear diffusion model with memory”, Comput. Math. Appl., 59:1 (2010), 254–273
Jangveladze T.A., Kiguradze Z.V., “Asymptotics for large time of solutions to nonlinear system associated with the penetration of a magnetic field into a substance”, Appl Math, 55:6 (2010), 471–493
Bai Yu., “Backward solutions to nonlinear integro-differential systems”, Cent Eur J Math, 8:4 (2010), 807–815
Jangveladze T., Kiguradze Z., Neta B., “Large time behavior of solutions to a nonlinear integro-differential system”, J. Math. Anal. Appl., 351:1 (2009), 382–391
Jangveladze T., Kiguradze Z., Neta B., “Finite difference approximation of a nonlinear integro-differential system”, Appl. Math. Comput., 215:2 (2009), 615–628
Jangveladze T., Kiguradze Z., “Large time behavior of solutions to one nonlinear integro-differential equation”, Georgian Math. J., 15:3 (2008), 531–539
Dzhangveladze T.A., Kiguradze Z.V., “Asymptotic behavior of the solution of a nonlinear integro-differential diffusion equation”, Differ. Equ., 44:4 (2008), 538–550