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Deadlines
(Previous Conference: PM-AM 2016, Vienna, Austria, January 15-17, 2016)
PLENARY SPEAKERS:
Prof. Temur Jangveladze (Dzhangveladze), Ilia Vekua Institute of Applied Mathematics of Ivane Javakhishvili Tbilisi State University, Department of Mathematics of Georgian Technical University, Georgia, e-mail: tjangv@yahoo.com
Title: "Investigation and Approximate Solution of Two Systems of Nonlinear Partial Differential Equations"
Abstract: In mathematical modeling of many natural processes systems of partial differential equations arise very often. Most of these models are nonlinear. This circumstance significantly complicate the study of such models. Investigation and approximate solution of the initial-boundary value problems posed for these systems are the actual sphere of contemporary mathematical physics and numerical analysis. One such type important model is obtained at mathematical modeling of processes of electro-magnetic field penetration in the substance. In the quasi-stationary approximation, this diffusion process, taking into account of Joule law is described by nonlinear system of Maxwell equations. For more thorough description of electromagnetic field propagation in the medium, it is desirable to take into consideration different physical effects, first of all - heat conductivity of the medium. In this case, with taking into account again the Joule law, the different type nonlinear system of partial differential equations is obtained. Many scientific papers are devoted to the investigation and approximate solution of abovementioned differential models. Many authors are studying convergence of semi-discrete analogs and finite-difference schemes for the models described here and for the problems similar to them. There are still many open questions in this direction. We study some properties of solutions of different kind of initial-boundary value problems for investigated systems, as well as numerical solution of those problems. We compare theoretical results to numerical ones. Special attention is paid to construction of discrete analogs, corresponding to one-dimensional models as well as to construction, analysis and computer realization of decomposition algorithms with respect to physical processes for the second system. The above-mentioned decomposition is defined by splitting this model in two parts: in the first part the Joule heat release is taken into account and in the second - part the heat conductivity of the medium is considered.