Global existence and uniform stability of solutions for a quasilinear viscoelastic problem
Abstract In this paper the nonlinear viscoelastic wave equation in canonical form |ut|ρutt − ∆u − ∆utt + � t 0 g(t − τ)∆u(τ )dτ = b|u|p−2u with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the vis...
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2020
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| Online Access: | https://eprints.kfupm.edu.sa/id/eprint/520/1/MMASRevised.pdf |
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| _version_ | 1864513388820824064 |
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| author | Messaoudi, Salim A. |
| author2 | Tatar, Nasser-eddine unknown |
| author2_role | author author |
| author_facet | Messaoudi, Salim A. Tatar, Nasser-eddine unknown |
| author_role | author |
| dc.creator.none.fl_str_mv | Messaoudi, Salim A. Tatar, Nasser-eddine unknown |
| dc.date.*.fl_str_mv | 2020 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://eprints.kfupm.edu.sa/id/eprint/520/1/MMASRevised.pdf Global existence and uniform stability of solutions for a quasilinear viscoelastic problem. MATHEMATICAL METHODS IN THE APPLIED SCIENCES 30 (6). |
| dc.language.none.fl_str_mv | en |
| dc.relation.none.fl_str_mv | https://eprints.kfupm.edu.sa/id/eprint/520/ |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Math |
| dc.title.none.fl_str_mv | Global existence and uniform stability of solutions for a quasilinear viscoelastic problem |
| dc.type.none.fl_str_mv | Article PeerReviewed info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | Abstract In this paper the nonlinear viscoelastic wave equation in canonical form |ut|ρutt − ∆u − ∆utt + � t 0 g(t − τ)∆u(τ )dτ = b|u|p−2u with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniformly decay of solutions provided that the initial data are in some stable set. Keywords and phrases: Global existence, Exponential decay, Nonlinear source, Relaxation function, Polynomial decay, Viscoelasticity. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | KFUPM_936d57d62aec25483e7c11ecc1fba40e |
| identifier_str_mv | Global existence and uniform stability of solutions for a quasilinear viscoelastic problem. MATHEMATICAL METHODS IN THE APPLIED SCIENCES 30 (6). |
| language_invalid_str_mv | en |
| network_acronym_str | KFUPM |
| network_name_str | King Fahd University of Petroleum and Minerals |
| oai_identifier_str | oai::520 |
| publishDate | 2020 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Global existence and uniform stability of solutions for a quasilinear viscoelastic problemMessaoudi, Salim A.Tatar, Nasser-eddineunknownMathAbstract In this paper the nonlinear viscoelastic wave equation in canonical form |ut|ρutt − ∆u − ∆utt + � t 0 g(t − τ)∆u(τ )dτ = b|u|p−2u with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniformly decay of solutions provided that the initial data are in some stable set. Keywords and phrases: Global existence, Exponential decay, Nonlinear source, Relaxation function, Polynomial decay, Viscoelasticity.ArticlePeerReviewedinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://eprints.kfupm.edu.sa/id/eprint/520/1/MMASRevised.pdf Global existence and uniform stability of solutions for a quasilinear viscoelastic problem. MATHEMATICAL METHODS IN THE APPLIED SCIENCES 30 (6). enhttps://eprints.kfupm.edu.sa/id/eprint/520/2020info:eu-repo/semantics/openAccessoai::5202019-11-01T13:24:12Z |
| spellingShingle | Global existence and uniform stability of solutions for a quasilinear viscoelastic problem Messaoudi, Salim A. Math |
| status_str | publishedVersion |
| title | Global existence and uniform stability of solutions for a quasilinear viscoelastic problem |
| title_full | Global existence and uniform stability of solutions for a quasilinear viscoelastic problem |
| title_fullStr | Global existence and uniform stability of solutions for a quasilinear viscoelastic problem |
| title_full_unstemmed | Global existence and uniform stability of solutions for a quasilinear viscoelastic problem |
| title_short | Global existence and uniform stability of solutions for a quasilinear viscoelastic problem |
| title_sort | Global existence and uniform stability of solutions for a quasilinear viscoelastic problem |
| topic | Math |
| url | https://eprints.kfupm.edu.sa/id/eprint/520/1/MMASRevised.pdf |