$Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian$
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Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory....

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Autores principales:	Bidi Younes, Beniani Abderrahmane, Zennir Khaled, Himadan Ahmed
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	fractional laplacian global existence fractional sobolev spaces potential well hyperbolic problem 35r11 35l20 35l70 47g20 35q91 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/133009d19c1045f295e3f2b9810a3b5c
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spelling	oai:doaj.org-article:133009d19c1045f295e3f2b9810a3b5c2021-12-05T14:10:45ZGlobal existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian2391-466110.1515/dema-2021-0022https://doaj.org/article/133009d19c1045f295e3f2b9810a3b5c2021-07-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0022https://doaj.org/toc/2391-4661We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.Bidi YounesBeniani AbderrahmaneZennir KhaledHimadan AhmedDe Gruyterarticlefractional laplacianglobal existencefractional sobolev spacespotential wellhyperbolic problem35r1135l2035l7047g2035q91MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 245-258 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	fractional laplacian global existence fractional sobolev spaces potential well hyperbolic problem 35r11 35l20 35l70 47g20 35q91 Mathematics QA1-939
spellingShingle	fractional laplacian global existence fractional sobolev spaces potential well hyperbolic problem 35r11 35l20 35l70 47g20 35q91 Mathematics QA1-939 Bidi Younes Beniani Abderrahmane Zennir Khaled Himadan Ahmed Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian
description	We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.
format	article
author	Bidi Younes Beniani Abderrahmane Zennir Khaled Himadan Ahmed
author_facet	Bidi Younes Beniani Abderrahmane Zennir Khaled Himadan Ahmed
author_sort	Bidi Younes
title	Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian
title_short	Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian
title_full	Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian
title_fullStr	Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian
title_full_unstemmed	Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian
title_sort	global existence and dynamic structure of solutions for damped wave equation involving the fractional laplacian
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/133009d19c1045f295e3f2b9810a3b5c
work_keys_str_mv	AT bidiyounes globalexistenceanddynamicstructureofsolutionsfordampedwaveequationinvolvingthefractionallaplacian AT benianiabderrahmane globalexistenceanddynamicstructureofsolutionsfordampedwaveequationinvolvingthefractionallaplacian AT zennirkhaled globalexistenceanddynamicstructureofsolutionsfordampedwaveequationinvolvingthefractionallaplacian AT himadanahmed globalexistenceanddynamicstructureofsolutionsfordampedwaveequationinvolvingthefractionallaplacian
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Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

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