On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate

A system of partial differential equations with integral terms which take into account hereditary effects is considered. The system describes a behaviour of thermoviscoelastic plate with Berger's type of nonlinearity. The hereditary effect is taken into account both in the temperature variable...

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Бібліографічні деталі
Дата:2010
Автор: Potomkin, M.
Формат: Стаття
Мова:English
Опубліковано: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2010
Назва видання:Журнал математической физики, анализа, геометрии
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/106648
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate / M. Potomkin // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 3. — С. 305-336. — Бібліогр.: 25 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-106648
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spelling irk-123456789-1066482016-10-02T03:02:56Z On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate Potomkin, M. A system of partial differential equations with integral terms which take into account hereditary effects is considered. The system describes a behaviour of thermoviscoelastic plate with Berger's type of nonlinearity. The hereditary effect is taken into account both in the temperature variable and in the bending one. The main goal of the paper is to analyze the passage to the singular limit when memory kernels collapse into the Dirac mass. In particular, it is proved that the solutions to the system with memory are close in some sense to the solutions to the corresponding memory-free limiting system. Besides, the upper semicontinuity of the family of attractors with respect to the singular limit is obtained. 2010 Article On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate / M. Potomkin // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 3. — С. 305-336. — Бібліогр.: 25 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106648 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description A system of partial differential equations with integral terms which take into account hereditary effects is considered. The system describes a behaviour of thermoviscoelastic plate with Berger's type of nonlinearity. The hereditary effect is taken into account both in the temperature variable and in the bending one. The main goal of the paper is to analyze the passage to the singular limit when memory kernels collapse into the Dirac mass. In particular, it is proved that the solutions to the system with memory are close in some sense to the solutions to the corresponding memory-free limiting system. Besides, the upper semicontinuity of the family of attractors with respect to the singular limit is obtained.
format Article
author Potomkin, M.
spellingShingle Potomkin, M.
On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate
Журнал математической физики, анализа, геометрии
author_facet Potomkin, M.
author_sort Potomkin, M.
title On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate
title_short On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate
title_full On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate
title_fullStr On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate
title_full_unstemmed On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate
title_sort on singular limit and upper semicontinuous family of attractors of thermoviscoelastic berger plate
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2010
url http://dspace.nbuv.gov.ua/handle/123456789/106648
citation_txt On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate / M. Potomkin // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 3. — С. 305-336. — Бібліогр.: 25 назв. — англ.
series Журнал математической физики, анализа, геометрии
work_keys_str_mv AT potomkinm onsingularlimitanduppersemicontinuousfamilyofattractorsofthermoviscoelasticbergerplate
first_indexed 2023-10-18T20:13:24Z
last_indexed 2023-10-18T20:13:24Z
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