Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms
In this paper, a nonlinear viscoelastic Kirchhoff equation in a bounded domain with a time-varying delay term and logarithmic nonlinearity in the weakly nonlinear internal feedback is considered, where the global and local existence of solutions in suitable Sobolev spaces by means of the energy meth...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/7105387 |
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| _version_ | 1832566436920295424 |
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| author | Nadia Mezouar Salah Mahmoud Boulaaras Ali Allahem |
| author_facet | Nadia Mezouar Salah Mahmoud Boulaaras Ali Allahem |
| author_sort | Nadia Mezouar |
| collection | DOAJ |
| description | In this paper, a nonlinear viscoelastic Kirchhoff equation in a bounded domain with a time-varying delay term and logarithmic nonlinearity in the weakly nonlinear internal feedback is considered, where the global and local existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo-Galerkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given. These results extend and improve many results in the literature. |
| format | Article |
| id | doaj-art-c1423c1bc10c459ab35cd856d8d78d8c |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-c1423c1bc10c459ab35cd856d8d78d8c2025-02-03T01:04:15ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/71053877105387Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source TermsNadia Mezouar0Salah Mahmoud Boulaaras1Ali Allahem2Faculty of Sciences Economics, Mustapha Stambouli University, Mascara 29000, AlgeriaDepartment of Mathematics, College of Sciences and Arts, Qassim University, Al-Rass, Saudi ArabiaDepartment of Mathematics, College of Sciences, Qassim University, Buraydah, Saudi ArabiaIn this paper, a nonlinear viscoelastic Kirchhoff equation in a bounded domain with a time-varying delay term and logarithmic nonlinearity in the weakly nonlinear internal feedback is considered, where the global and local existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo-Galerkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given. These results extend and improve many results in the literature.http://dx.doi.org/10.1155/2020/7105387 |
| spellingShingle | Nadia Mezouar Salah Mahmoud Boulaaras Ali Allahem Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms Complexity |
| title | Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms |
| title_full | Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms |
| title_fullStr | Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms |
| title_full_unstemmed | Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms |
| title_short | Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms |
| title_sort | global existence of solutions for the viscoelastic kirchhoff equation with logarithmic source terms |
| url | http://dx.doi.org/10.1155/2020/7105387 |
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