Издательский центр ЮУрГУ, 2016 c South Ural State University Main purpose of the publication is to promote the union of the qualitative of numerical studies of mathematical models. <...> Editorial Board A.V. Keller, South Ural State University, Chelyabinsk, Russian Federation N.A. Manakova, South Ural State University, Chelyabinsk, Russian Federation G.A. Sviridyuk, South Ural State University, Chelyabinsk, Russian Federation V.I. Zalyapin, South Ural State University, Chelyabinsk, Russian Federation A.A. Zamyshlyaeva, South Ural State University, Chelyabinsk, Russian Federation Editorial Council J. Banasiak, University of Pretoria, Pretoria, Republic of South Africa M.M. Brzhezinskaya, Helmholtz-Zentrum Berlin for Materials and Energy, Berlin, Germany A.G. Chentsov, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the RAS, Yekaterinburg, Russian Federation A.V. Fursikov, Lomonosov Moscow State University, Moscow, Russian Federation A. Favini, University of Bologna, Bologna, Italy V.V. Jikov, Vladimir State University named after Alexander and Nikolay Stoletovs, Vladimir, Russian Federation S.I. Kadchenko, Nosov Magnitogorsk State Technical University, Magnitogorsk, Russian Federation T.Sh. <...> Kal'menov, Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan M.O. Korpusov, Lomonosov Moscow State University, Moscow, Russian Federation A.I. Kozhanov, Sobolev Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk, Russian Federation D.A. Novikov, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation B.T. Polyak, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation H.K. Radev, Technical University of So a, So a, Bulgaria Yu. <...> Zeldovich, University of Central Florida, Orlando, United States of America P.J.Y. Wong, Nanyang Technological University, School of Electrical and Electronic Engineering, Singapore Yong Li, College of Electrical and Information Engineering, Hunan University, Changsha, China 76, Lenin ave, Chelyabinsk, 454080, Russian Federation, vestnik@susu.ru, mmp.vestnik.susu.ru Содержание Математическое моделирование ON ONE MATHEMATICAL MODEL OF THE EXTRACTION PROCESS OF POLYDISPERSE POROUS MATERIAL N.E. Erzhanov, I. Orazov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 <...>
Вестник_Южно-Уральского_государственного_университета._Серия_Математическое_моделирование_и_программирование_№2_2016.pdf
Учредитель Федеральное государственное бюджетное образовательное
учреждение высшего профессионального образования
≪
Южно-Уральский государственный университет≫
(национальный исследовательский университет)
Основной целью издания является пропаганда союза качественных и численных исследований
математических моделей. Предпочтение при публикации будут иметь статьи, посвященные
результатам качественных исследований математических моделей, выявляющих
какие-либо неочевидные их свойства; результатам численных исследований, содержащих
разработки новых вычислительных алгоритмов применительно к математическим моделям;
комплексам программ, созданным для постановки вычислительных экспериментов.
Редакционная коллегия
ê.ô.-ì.í., ïðîô. Заляпин Â.È.,
ä.ô.-ì.í., äîö. Замышляева À.À.,
ä.ô.-ì.í., äîö. Келлер À.Â.,
ê.ô.-ì.í., äîö. Манакова Í.À.
(отв. секретарь),
ä.ô.-ì.í., ïðîô. Свиридюк Ã.À.
(отв. редактор)
Редакционный совет
ä.ô.-ì.í., ïðîô. Банасяк ß.,
ä.ô.-ì.í. Бржезинская Ì.Ì.,
ä.ô.-ì.í., àêàä. РАН Васильев Ñ.Í.
(председатель),
ä.ò.í., ïðîô. Володарский Å.Ò.,
ïðîô. Вонг Ï.,
ä.ô.-ì.í., ïðîô. Жиков Â.Â.,
ä.ô.-ì.í., ÷ë.-êîð. РАН Зельдович Á.ß.,
проф. Йонг Ли,
ä.ô.-ì.í., ïðîô. Кадченко Ñ.È.,
ä.ô.-ì.í., àêàä. НАН Республики
Казахстан Кальменов Т.Ш.,
ä.ô.-ì.í., ïðîô. Кожанов À.È.,
ä.ô.-ì.í., äîö. Корпусов Ì.Î.,
ä.ò.í., ÷ë.-êîð. РАН Новиков Ä.À.,
ä.ò.í., ñ.í.ñ. Поляк Á.Ò.,
ä.ò.í., ïðîô. Радев Õ.Ê.,
ä.ô.-ì.í., ïðîô. Сапронов Þ.È.,
ïðîô. Tà Зуй Ôûîíã,
доктор, проф. Фавини А.,
ä.ô.-ì.í., ïðîô. Фурсиков À.Â.,
ä.ô.-ì.í., ÷ë.-êîð. РАН Ченцов À.Ã.,
ä.ô.-ì.í., ïðîô. Штраус Â.À.
⃝ Издательский центр ÞÓðÃÓ, 2016
c
Стр.1
South Ural State University
Main purpose of the publication is to promote the union of the qualitative of numerical studies of
mathematical models. Articles, devoted to the results of qualitative studies of mathematical models, that
identify any non-obvious properties, the results of numerical studies that contain the development of
new computational algorithms applied for the computational experiments, will have the preference for
publication.
Editorial Board
A.V. Keller, South Ural State University, Chelyabinsk, Russian Federation
N.A. Manakova, South Ural State University, Chelyabinsk, Russian Federation
G.A. Sviridyuk, South Ural State University, Chelyabinsk, Russian Federation
V.I. Zalyapin, South Ural State University, Chelyabinsk, Russian Federation
A.A. Zamyshlyaeva, South Ural State University, Chelyabinsk, Russian Federation
Editorial Council
J. Banasiak, University of Pretoria, Pretoria, Republic of South Africa
M.M. Brzhezinskaya, Helmholtz-Zentrum Berlin for Materials and Energy, Berlin, Germany
A.G. Chentsov, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the RAS,
Yekaterinburg, Russian Federation
A.V. Fursikov, Lomonosov Moscow State University, Moscow, Russian Federation
A. Favini, University of Bologna, Bologna, Italy
V.V. Jikov, Vladimir State University named after Alexander and Nikolay Stoletovs, Vladimir, Russian
Federation
S.I. Kadchenko, Nosov Magnitogorsk State Technical University, Magnitogorsk, Russian Federation
T.Sh. Kal'menov, Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan
M.O. Korpusov, Lomonosov Moscow State University, Moscow, Russian Federation
A.I. Kozhanov, Sobolev Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk,
Russian Federation
D.A. Novikov, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation
B.T. Polyak, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation
H.K. Radev, Technical University of So a, So a, Bulgaria
Yu.I. Sapronov, Voronezh State University, Voronezh, Russian Federation
V.A. Strauss, Simon Bolivar University, Caracas, Venezuela
Ta Duy Phuong, Hanoi Institute of Mathematics, Hanoi, Vietnam
S.N. Vassilyev, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation
E.T. Volodarskiy, National Technical University, Kiev, Ukraine
B.Ya. Zeldovich, University of Central Florida, Orlando, United States of America
P.J.Y. Wong, Nanyang Technological University, School of Electrical and Electronic Engineering,
Singapore
Yong Li, College of Electrical and Information Engineering, Hunan University, Changsha, China
76, Lenin ave, Chelyabinsk, 454080, Russian Federation, vestnik@susu.ru, mmp.vestnik.susu.ru
Стр.2
Содержание
Математическое моделирование
ON ONE MATHEMATICAL MODEL OF THE EXTRACTION PROCESS
OF POLYDISPERSE POROUS MATERIAL
N.E. Erzhanov, I. Orazov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
ВОЗНИКНОВЕНИЕ АВТОКОЛЕБАНИЙ В СИСТЕМЕ РЭЛЕЯ С ДИФФУЗИЕЙ
À.Â. Казарников, Ñ.Â. Ревина . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ВЛИЯНИЯ СХЕМНОЙ ВЯЗКОСТИ
ЧИСЛЕННЫХ МЕТОДОВ НА ВЕЛИЧИНУ ИМПУЛЬСА, ПЕРЕДАВАЕМОГО
УДАРНЫМИ ВОЛНАМИ
Þ.Ì. Êîâàëåâ, Å.Å. Пигасов . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
ОБРАТНЫЕ ЗАДАЧИ ОПРЕДЕЛЕНИЯ ГРАНИЧНЫХ РЕЖИМОВ
ДЛЯ НЕКОТОРЫХ УРАВНЕНИЙ СОБОЛЕВСКОГО ТИПА
À.È. Кожанов . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
МЕТОД НЕГЛАДКИХ ИНТЕГРАЛЬНЫХ НАПРАВЛЯЮЩИХ ФУНКЦИЙ
В ЗАДАЧЕ О СУЩЕСТВОВАНИИ ПЕРИОДИЧЕСКИХ РЕШЕНИЙ
ВКЛЮЧЕНИЙ С КАУЗАЛЬНЫМИ ОПЕРАТОРАМИ
Ñ.Â. Корнев . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
STATIONARY SOLUTIONS FOR THE CAHN HILLIARD EQUATION COUPLED
WITH NEUMANN BOUNDARY CONDITIONS
I.B. Krasnyuk, R.M. Taranets, M. Chugunova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
INVERSE PROBLEMS FOR SOME SOBOLEV-TYPE MATHEMATICAL MODELS
S.G. Pyatkov, S.N. Shergin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
ACTIVE PARAMETRIC IDENTIFICATION OF GAUSSIAN LINEAR DISCRETE
SYSTEM BASED ON EXPERIMENT DESIGN
V.M. Chubich, O.S. Chernikova, E.A. Beriket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Краткие сообщения
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ РЕАКЦИИ ИММУННОЙ СИСТЕМЫ
НА ОПУХОЛЬ НА ОСНОВЕ УТОЧНЕННОЙ МОДЕЛИ РЕШИНЬО И ДЕ ЛИЗИ
Í.È. Еремеева . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
ON A MODEL OF OSCILLATIONS OF A THIN FLAT PLATE WITH A VARIETY
OF MOUNTS ON OPPOSITE SIDES
U.A. Iskakova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
NUMERICAL RESEARCH OF THE BARENBLATT ZHELTOV COCHINA
STOCHASTIC MODEL
S.I.Kadchenko, Å.À. Soldatova, S.À. Zagrebina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
ON A HEAT AND MASS TRANSFER MODEL FOR THE LOCALLY
INHOMOGENEOUS INITIAL DATA
T.Sh. Kal'menov, G.D. Arepova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
MODELLING THE INNOVATION ACTIVITY OF AN ENTERPRISE
V.G. Mokhov, K.S. Stakhanov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
ABOUT TWO MODELS OF MODERN CHRONOLOGY. TO THE PROBLEM
OF HISTORY CHRONOLOGY
T.K. Plyshevskaya, E.M. Buriyak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Персоналии
СЕРГЕЙ ГРИГОРЬЕВИЧ ПЯТКОВ (Ê 60-ËÅÒÈÞ СО ДНЯ ÐÎÆÄÅÍÈß) . . . . . . . . . . . 139
Вестник ЮУрГУ. Серия ≪
и программирование≫
Математическое моделирование
(Âåñòíèê ЮУрГУ ÌÌÏ). 2016. Ò. 9, 2
Стр.3
Contents
Mathematical Modelling
ON ONE MATHEMATICAL MODEL OF THE EXTRACTION PROCESS
OF POLYDISPERSE POROUS MATERIAL
N.E. Erzhanov, I. Orazov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
THE ONSET OF AUTO-OSCILLATIONS IN RAYLEIGH SYSTEM WITH DIFFUSION
A.V. Kazarnikov, S.V. Revina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
MATHEMATICAL MODELLING OF INFLUENCE OF CIRCUIT VISCOSITY
OF NUMERICAL METHODS ON A VALUE OF THE IMPULSE TRANSFERRED
BY SHOCK WAVES
Yu.M. Kovalev, E.E. Pigasov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
INVERSE PROBLEMS FOR DETERMINING BOUNDARY REGIMES FOR SOME
EQUATIONS OF SOBOLEV TYPE
A.I. Kozhanov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
METHOD OF NONSMOOTH INTEGRAL GUIDING FUNCTIONS IN PERIODIC
SOLUTIONS PROBLEM FOR INCLUSIONS WITH CAUSAL MULTIOPERATORS
S.V. Kornev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
STATIONARY SOLUTIONS FOR THE CAHN HILLIARD EQUATION COUPLED
WITH NEUMANN BOUNDARY CONDITIONS
I.B. Krasnyuk, R.M. Taranets, M. Chugunova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
INVERSE PROBLEMS FOR SOME SOBOLEV-TYPE MATHEMATICAL MODELS
S.G. Pyatkov, S.N. Shergin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
ACTIVE PARAMETRIC IDENTIFICATION OF GAUSSIAN LINEAR DISCRETE
SYSTEM BASED ON EXPERIMENT DESIGN
V.M. Chubich, O.S. Chernikova, E.A. Beriket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Short Notes
NUMERICAL MODELLING OF THE REACTION OF THE IMMUNE SYSTEM
TO THE TUMOR BASED ON THE REVISED MODEL OF RESIGNO AND DE LISI
N.I. Eremeeva . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
ON A MODEL OF OSCILLATIONS OF A THIN FLAT PLATE WITH A VARIETY
OF MOUNTS ON OPPOSITE SIDES
U.A. Iskakova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
NUMERICAL RESEARCH OF THE BARENBLATT ZHELTOV COCHINA
STOCHASTIC MODEL
S.I.Kadchenko, Å.À. Soldatova, S.À. Zagrebina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
ON A HEAT AND MASS TRANSFER MODEL FOR THE LOCALLY
INHOMOGENEOUS INITIAL DATA
T.Sh. Kal'menov, G.D. Arepova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
MODELLING THE INNOVATION ACTIVITY OF AN ENTERPRISE
V.G. Mokhov, K.S. Stakhanov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
ABOUT TWO MODELS OF MODERN CHRONOLOGY. TO THE PROBLEM
OF HISTORY CHRONOLOGY
T.K. Plyshevskaya, E.M. Buriyak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Personalia
SERGEY GRIGORIEVICH PYATKOV (TO THE 60th ANNIVERSARY) . . . . . . . . . . . . . . . 139
Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming
& Computer Software (Bulletin SUSU MMCS), 2016, vol. 9, no. 2
Стр.4