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ერთი არაწრფივი კერძოწარმოებულებიანი ინტეგრო-დიფერენციალური განტოლების ამონახსნის ასიმპტოტური ყოფაქცევა დროითი ცვლადის უსასრულოდ ზრდისას და ნახევრად-დისკრეტული სქემის შესახებ (ფლორიდა, აშშ) (2014_tr_405)


დამფინანსებელი

SRNSFGშოთა რუსთაველის საქართველოს ეროვნული სამეცნიერო ფონდი

დაწყების თარიღი: 2014-03-28       დასრულების თარიღი: 2014-03-31

Non-linear differential and integro-differential equations and systems describe various processes in physical, economic, chemical, technological, and other sciences. Undoubtedly, it is very important to study the qualitative and structural characteristics of the solutions of initial-boundary value problems of these equations and systems; construct and study discrete analogs; and investigate numerical algorithms. Systems of integro-differential equations arise, for example, in mathematical modeling of the process of propagation of the magnetic field into a substance.
in the paper by Gordeziani D.G., Dzhangveladze T.A., Korshia T.K. Existence and Uniqueness of a Solution of Certain Nonlinear Parabolic Problems. Dfferential'nye Uravnenyia, 1983, V.19, N7, p.1197-1207, the reduction of the well-known system of Maxwell equations to the integro-differential form is shown.
In the work by Laptev G.I. Quasilinear Evolution Partial Differential Equations with Operator Coefficients. Doctoral Dissertation, Moscow, 1990 (Russian), a generalization of the above-mentioned model is given. In particular, if the temperature along the body is considered to be a constant, i.e. dependent on time and independent of spatial variables, then the so-called averaged integro-differential model is obtained to model the process of magnetic field propagation.
For such a one-dimensional averaged integro-differential model, the large time behavior of the solution of the initial-boundary value problem is investigated. The convergence of the corresponding semidiscrete scheme for the case of nonlinearity, which extends the previously studied cases, is also studied.

პროექტში მონაწილე პერსონალი:

მოხსენებები

  • Large Time Behavior and SemiDiscrete Scheme for One Nonlinear Partial Integro-Differential Equation, by Temur Jangveladze (Speaker), Zurab Kiguradze, Mikheil Gagoshidze at SIAM SEAS Conference, Florida Institute of Technology Melbourne, USA, Florida, March 29-30, 2014. SIAM Abstracts Book, 2014, p.47., 2014, Florida, USA.
  • On One Nonlinear Averaged Integro-Differential System with Source Terms, by Maia Aptsiauri (Speaker), Mikheil Gagoshidze at XXVIII Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), 2014, Tbilisi, Georgia.