Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations
In this work, we consider an initial-boundary value problem related to the nonlinear coupled viscoelastic equations \[ \left\{ \begin{array}{c} \left\vert u_{t}\right\vert ^{j}u_{tt}-\Delta u_{tt}-div\left( \left\vert \nabla u\right\vert ^{\alpha -2}\nabla u\right) -\Delta u+\int\limits_{0}^{t}g\lef...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2019-06-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/746892 |
| _version_ | 1827377628351299584 |
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| author | Şeyhmus Altındağ Erhan Pişkin |
| author_facet | Şeyhmus Altındağ Erhan Pişkin |
| author_sort | Şeyhmus Altındağ |
| collection | DOAJ |
| description | In this work, we consider an initial-boundary value problem related to the nonlinear coupled viscoelastic equations \[ \left\{ \begin{array}{c} \left\vert u_{t}\right\vert ^{j}u_{tt}-\Delta u_{tt}-div\left( \left\vert \nabla u\right\vert ^{\alpha -2}\nabla u\right) -\Delta u+\int\limits_{0}^{t}g\left( t-s\right) \Delta uds+\left\vert u_{t}\right\vert ^{m-1}u_{t}=f_{1}\left( u,v\right) ,\text{ } \\ \left\vert v_{t}\right\vert ^{j}v_{tt}-\Delta v_{tt}-div\left( \left\vert \nabla v\right\vert ^{\beta -2}\nabla v\right) -\Delta v+\int\limits_{0}^{t}h\left( t-s\right) \Delta vds+\left\vert v_{t}\right\vert ^{r-1}v_{t}=f_{2}\left( u,v\right) .\text{ } \end{array} \right. \] We will show the exponential growth of solutions with positive initial energy. |
| first_indexed | 2024-03-08T12:41:59Z |
| format | Article |
| id | doaj.art-fae1280e9f674a8f8d45d65ea4ca3417 |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:41:59Z |
| publishDate | 2019-06-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-fae1280e9f674a8f8d45d65ea4ca34172024-01-21T10:08:07ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532019-06-0122707810.32323/ujma.4845321225Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave EquationsŞeyhmus AltındağErhan Pişkin0DİCLE ÜNİVERSİTESİIn this work, we consider an initial-boundary value problem related to the nonlinear coupled viscoelastic equations \[ \left\{ \begin{array}{c} \left\vert u_{t}\right\vert ^{j}u_{tt}-\Delta u_{tt}-div\left( \left\vert \nabla u\right\vert ^{\alpha -2}\nabla u\right) -\Delta u+\int\limits_{0}^{t}g\left( t-s\right) \Delta uds+\left\vert u_{t}\right\vert ^{m-1}u_{t}=f_{1}\left( u,v\right) ,\text{ } \\ \left\vert v_{t}\right\vert ^{j}v_{tt}-\Delta v_{tt}-div\left( \left\vert \nabla v\right\vert ^{\beta -2}\nabla v\right) -\Delta v+\int\limits_{0}^{t}h\left( t-s\right) \Delta vds+\left\vert v_{t}\right\vert ^{r-1}v_{t}=f_{2}\left( u,v\right) .\text{ } \end{array} \right. \] We will show the exponential growth of solutions with positive initial energy.https://dergipark.org.tr/tr/download/article-file/746892viscoelastic wave equationsexponential growthnonlinear damping termviscoelastic wave equations |
| spellingShingle | Şeyhmus Altındağ Erhan Pişkin Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations Universal Journal of Mathematics and Applications viscoelastic wave equations exponential growth nonlinear damping term viscoelastic wave equations |
| title | Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations |
| title_full | Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations |
| title_fullStr | Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations |
| title_full_unstemmed | Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations |
| title_short | Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations |
| title_sort | exponential growth of solutions for nonlinear coupled viscoelastic wave equations |
| topic | viscoelastic wave equations exponential growth nonlinear damping term viscoelastic wave equations |
| url | https://dergipark.org.tr/tr/download/article-file/746892 |
| work_keys_str_mv | AT seyhmusaltındag exponentialgrowthofsolutionsfornonlinearcoupledviscoelasticwaveequations AT erhanpiskin exponentialgrowthofsolutionsfornonlinearcoupledviscoelasticwaveequations |