Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation
The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form under suitable assumptions on . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissip...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/716740 |
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| _version_ | 1832564019688374272 |
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| author | Daewook Kim Dojin Kim Keum-Shik Hong Il Hyo Jung |
| author_facet | Daewook Kim Dojin Kim Keum-Shik Hong Il Hyo Jung |
| author_sort | Daewook Kim |
| collection | DOAJ |
| description | The first objective of this paper is to prove the existence and uniqueness of
global solutions for a Kirchhoff-type wave equation with nonlinear dissipation
of the form under suitable assumptions on . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given. |
| format | Article |
| id | doaj-art-e480b2bdbd464c4cab559c67c993e5b1 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-e480b2bdbd464c4cab559c67c993e5b12025-02-03T01:12:06ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/716740716740Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear DissipationDaewook Kim0Dojin Kim1Keum-Shik Hong2Il Hyo Jung3Department of Mathematics, Pusan National University, 30 Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of KoreaDepartment of Mathematics, Oregon State University, Corvallis, OR 97331, USADepartment of Cogno-Mechatronics Engineering and School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of KoreaDepartment of Mathematics, Pusan National University, 30 Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of KoreaThe first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form under suitable assumptions on . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.http://dx.doi.org/10.1155/2014/716740 |
| spellingShingle | Daewook Kim Dojin Kim Keum-Shik Hong Il Hyo Jung Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation The Scientific World Journal |
| title | Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation |
| title_full | Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation |
| title_fullStr | Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation |
| title_full_unstemmed | Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation |
| title_short | Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation |
| title_sort | global existence and energy decay rates for a kirchhoff type wave equation with nonlinear dissipation |
| url | http://dx.doi.org/10.1155/2014/716740 |
| work_keys_str_mv | AT daewookkim globalexistenceandenergydecayratesforakirchhofftypewaveequationwithnonlineardissipation AT dojinkim globalexistenceandenergydecayratesforakirchhofftypewaveequationwithnonlineardissipation AT keumshikhong globalexistenceandenergydecayratesforakirchhofftypewaveequationwithnonlineardissipation AT ilhyojung globalexistenceandenergydecayratesforakirchhofftypewaveequationwithnonlineardissipation |