Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source
This paper considers the fuzzy viscoelastic model with a nonlinear source utt+Lu+∫0tgt−ζΔuζdζ−uγu−ηΔut=0 in a bounded field Ω. Under weak assumptions of the function gt, with the aid of Mathematica software, the computational technique is used to construct the auxiliary functionals and precise prior...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8615149 |
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| _version_ | 1832563339153113088 |
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| author | Fengyun Zhang |
| author_facet | Fengyun Zhang |
| author_sort | Fengyun Zhang |
| collection | DOAJ |
| description | This paper considers the fuzzy viscoelastic model with a nonlinear source utt+Lu+∫0tgt−ζΔuζdζ−uγu−ηΔut=0 in a bounded field Ω. Under weak assumptions of the function gt, with the aid of Mathematica software, the computational technique is used to construct the auxiliary functionals and precise priori estimates. As time goes to infinity, we prove that the solution is global and energy decays to zero in two different ways: the exponential form and the polynomial form. |
| format | Article |
| id | doaj-art-13f810f24dc54739903dd03ab9a4182b |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-13f810f24dc54739903dd03ab9a4182b2025-02-03T01:20:20ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/86151498615149Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear SourceFengyun Zhang0Department of Mathematics, Jining University, Qufu 273155, ChinaThis paper considers the fuzzy viscoelastic model with a nonlinear source utt+Lu+∫0tgt−ζΔuζdζ−uγu−ηΔut=0 in a bounded field Ω. Under weak assumptions of the function gt, with the aid of Mathematica software, the computational technique is used to construct the auxiliary functionals and precise priori estimates. As time goes to infinity, we prove that the solution is global and energy decays to zero in two different ways: the exponential form and the polynomial form.http://dx.doi.org/10.1155/2020/8615149 |
| spellingShingle | Fengyun Zhang Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source Journal of Mathematics |
| title | Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source |
| title_full | Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source |
| title_fullStr | Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source |
| title_full_unstemmed | Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source |
| title_short | Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source |
| title_sort | uniform energy decay rates for the fuzzy viscoelastic model with a nonlinear source |
| url | http://dx.doi.org/10.1155/2020/8615149 |
| work_keys_str_mv | AT fengyunzhang uniformenergydecayratesforthefuzzyviscoelasticmodelwithanonlinearsource |