Attractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System

In this paper, we develop a general approach to investigate limit dynamics of infinite-dimensional dissipative impulsive systems whose initial conditions do not uniquely determine their long time behavior. Based on the notion of an uniform attractor, we show how to describe limit behavior of such co...

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Autores principales:	S. Dashkovskiy, O. A. Kapustian, O. V. Kapustyan, N. V. Gorban
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/f3d75ea368304639978d4ad76b6a4d3d
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spelling	oai:doaj.org-article:f3d75ea368304639978d4ad76b6a4d3d2021-11-15T01:19:39ZAttractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System1563-514710.1155/2021/7385450https://doaj.org/article/f3d75ea368304639978d4ad76b6a4d3d2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/7385450https://doaj.org/toc/1563-5147In this paper, we develop a general approach to investigate limit dynamics of infinite-dimensional dissipative impulsive systems whose initial conditions do not uniquely determine their long time behavior. Based on the notion of an uniform attractor, we show how to describe limit behavior of such complex systems with the help of properties of their components. More precisely, we prove the existence of the uniform attractor for an impulsive multivalued system in terms of properties of nonimpulsive semiflow and impulsive parameters. We also give an application of these abstract results to the impulsive reaction-diffusion system without uniqueness.S. DashkovskiyO. A. KapustianO. V. KapustyanN. V. GorbanHindawi LimitedarticleEngineering (General). Civil engineering (General)TA1-2040MathematicsQA1-939ENMathematical Problems in Engineering, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939 S. Dashkovskiy O. A. Kapustian O. V. Kapustyan N. V. Gorban Attractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System
description	In this paper, we develop a general approach to investigate limit dynamics of infinite-dimensional dissipative impulsive systems whose initial conditions do not uniquely determine their long time behavior. Based on the notion of an uniform attractor, we show how to describe limit behavior of such complex systems with the help of properties of their components. More precisely, we prove the existence of the uniform attractor for an impulsive multivalued system in terms of properties of nonimpulsive semiflow and impulsive parameters. We also give an application of these abstract results to the impulsive reaction-diffusion system without uniqueness.
format	article
author	S. Dashkovskiy O. A. Kapustian O. V. Kapustyan N. V. Gorban
author_facet	S. Dashkovskiy O. A. Kapustian O. V. Kapustyan N. V. Gorban
author_sort	S. Dashkovskiy
title	Attractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System
title_short	Attractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System
title_full	Attractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System
title_fullStr	Attractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System
title_full_unstemmed	Attractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System
title_sort	attractors for multivalued impulsive systems: existence and applications to reaction-diffusion system
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/f3d75ea368304639978d4ad76b6a4d3d
work_keys_str_mv	AT sdashkovskiy attractorsformultivaluedimpulsivesystemsexistenceandapplicationstoreactiondiffusionsystem AT oakapustian attractorsformultivaluedimpulsivesystemsexistenceandapplicationstoreactiondiffusionsystem AT ovkapustyan attractorsformultivaluedimpulsivesystemsexistenceandapplicationstoreactiondiffusionsystem AT nvgorban attractorsformultivaluedimpulsivesystemsexistenceandapplicationstoreactiondiffusionsystem
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Attractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System

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