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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Hindawi Limited
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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doaj-13f810f24dc54739903dd03ab9a4182b2020-11-25T04:03:27ZengHindawi LimitedJournal of Mathematics2314-47852020-01-01202010.1155/2020/86151498615149Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear SourceFengyun Zhang0Department of MathematicsThis 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Fengyun Zhang |
| spellingShingle |
Fengyun Zhang Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source Journal of Mathematics |
| author_facet |
Fengyun Zhang |
| author_sort |
Fengyun Zhang |
| title |
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_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_sort |
uniform energy decay rates for the fuzzy viscoelastic model with a nonlinear source |
| publisher |
Hindawi Limited |
| series |
Journal of Mathematics |
| issn |
2314-4785 |
| publishDate |
2020-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2020/8615149 |
| work_keys_str_mv |
AT fengyunzhang uniformenergydecayratesforthefuzzyviscoelasticmodelwithanonlinearsource |
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1715058087491010560 |