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

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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Main Authors:	Bidi Younes, Beniani Abderrahmane, Zennir Khaled, Himadan Ahmed
Format:	Article
Language:	English
Published:	De Gruyter 2021-07-01
Series:	Demonstratio Mathematica
Subjects:	fractional laplacian global existence fractional sobolev spaces potential well hyperbolic problem 35r11 35l20 35l70 47g20 35q91
Online Access:	https://doi.org/10.1515/dema-2021-0022

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spelling	doaj-133009d19c1045f295e3f2b9810a3b5c2021-09-22T06:13:05ZengDe GruyterDemonstratio Mathematica2391-46612021-07-0154124525810.1515/dema-2021-0022Global existence and dynamic structure of solutions for damped wave equation involving the fractional LaplacianBidi Younes0Beniani Abderrahmane1Zennir Khaled2Himadan Ahmed3University of Djillali Liabes B.P. 89, Didi bel Abbas 22000, AlgeriaLaboratory of Analysis and Control of Partial Differential Equations, University of Ain Temouchent Belhadj Bouchaib - B.P. 284 RP, Ain Temouchent 46000, AlgeriaDepartment of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Qassim, Saudi ArabiaDepartment of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Qassim, Saudi ArabiaWe 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.https://doi.org/10.1515/dema-2021-0022fractional laplacianglobal existencefractional sobolev spacespotential wellhyperbolic problem35r1135l2035l7047g2035q91
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bidi Younes Beniani Abderrahmane Zennir Khaled Himadan Ahmed
spellingShingle	Bidi Younes Beniani Abderrahmane Zennir Khaled Himadan Ahmed Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian Demonstratio Mathematica fractional laplacian global existence fractional sobolev spaces potential well hyperbolic problem 35r11 35l20 35l70 47g20 35q91
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
series	Demonstratio Mathematica
issn	2391-4661
publishDate	2021-07-01
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.
topic	fractional laplacian global existence fractional sobolev spaces potential well hyperbolic problem 35r11 35l20 35l70 47g20 35q91
url	https://doi.org/10.1515/dema-2021-0022
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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