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Akademgorodok, Russia

Denisenko V.V.,Institute of Computational Modeling
Journal of Applied and Industrial Mathematics | Year: 2012

A new mathematical model is proposed to describe the quasi-stationary atmospheric electric fields with an approximate consideration of the ionosphere conductivity. Under the assumption of verticality of the geomagnetic field, a two-dimensional model of the ionosphere conducting layer is used that is customary for the large-scale fields. Within the framework of this model, the ionosphere can be described by a special boundary condition in a boundary value problem for the atmospheric electric field. A linear boundary value problem is stated with a symmetric positive definite elliptic operator. The minimum principle is substantiated for the quadratic functional of energy. The existence and uniqueness of a generalized solution are proved. Under study is also the imprecision of the approximate description of the ionosphere conductor. © 2012 Pleiades Publishing, Ltd.


Gorban' A.N.,University of Leicester | Gorban' A.N.,Institute of Computational Modeling | Cheresiz V.M.,RAS Sobolev Institute of Mathematics
Journal of Applied and Industrial Mathematics | Year: 2010

We consider one-parameter semigroups of homeomorphisms depending continuously on the parameters. We study the phenomenon of slow relaxation that consists in anomalously slow motion to the limit sets. We investigate the connection between slow relaxations and bifurcations of limit sets and other singularities of the dynamics. The statements of some of the problems stem from mathematical chemistry. © Pleiades Publishing, Ltd., 2010.


Novikov E.A.,Institute of Computational Modeling
Journal of Applied and Industrial Mathematics | Year: 2010

The additive third order method for solving stiff nonautonomous problems is constructed. Some inequalities are obtained for controlling the calculation accuracy and stability of the numerical scheme. Calculation results are presented. © 2010 Pleiades Publishing, Ltd.


Gorban' A.N.,University of Leicester | Gorban' A.N.,Institute of Computational Modeling | Cheresiz V.M.,RAS Sobolev Institute of Mathematics
Journal of Applied and Industrial Mathematics | Year: 2011

We study connections between various types of slow relaxations of a dynamical system with the peculiarities of its behavior in the general situation when the phase space of the system is an arbitrary metric space, as well as in the case of a especial importance for applications when the phase space is a smooth manifold. © 2011 Pleiades Publishing, Ltd.


Gorban' A.N.,University of Leicester | Gorban' A.N.,Institute of Computational Modeling | Cheresiz V.M.,RAS Sobolev Institute of Mathematics
Journal of Applied and Industrial Mathematics | Year: 2010

We propose a number of approaches to the notion of the relaxation time of a dynamical system which are motivated by the problems of chemical kinetics, give exact mathematical definitions of slow relaxations, study their possible reasons, among which an important role is played by bifurcations of limit sets. © 2010 Pleiades Publishing, Ltd.

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