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....
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-07-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2021-0022 |
| _version_ | 1819001721103319040 |
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| author | Bidi Younes Beniani Abderrahmane Zennir Khaled Himadan Ahmed |
| author_facet | Bidi Younes Beniani Abderrahmane Zennir Khaled Himadan Ahmed |
| author_sort | Bidi Younes |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-20T22:53:42Z |
| format | Article |
| id | doaj.art-133009d19c1045f295e3f2b9810a3b5c |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-20T22:53:42Z |
| publishDate | 2021-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-133009d19c1045f295e3f2b9810a3b5c2022-12-21T19:24:10ZengDe 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 |
| 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 |
| title | 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_short | 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 |
| 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 |
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