Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping
We prove the existence and uniqueness of a global solution of a damped quasilinear hyperbolic equation. Key point to our proof is the use of the Yosida approximation. Furthermore, we apply a method based on a specific integral inequality to prove that the solution decays exponentially to zero when t...
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| Format: | Article |
| Language: | English |
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University of Szeged
1998-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=12 |
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doaj-906e0a558a4048f09ac614b1d2ee0f462021-07-14T07:21:17ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38751998-01-011998711210.14232/ejqtde.1998.1.712Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear dampingM. Aassila0Université Louis Pasteur et C.N.R.S., Strasbourg Cédex, FranceWe prove the existence and uniqueness of a global solution of a damped quasilinear hyperbolic equation. Key point to our proof is the use of the Yosida approximation. Furthermore, we apply a method based on a specific integral inequality to prove that the solution decays exponentially to zero when the time t goes to infinity.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=12 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. Aassila |
| spellingShingle |
M. Aassila Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping Electronic Journal of Qualitative Theory of Differential Equations |
| author_facet |
M. Aassila |
| author_sort |
M. Aassila |
| title |
Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping |
| title_short |
Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping |
| title_full |
Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping |
| title_fullStr |
Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping |
| title_full_unstemmed |
Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping |
| title_sort |
asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping |
| publisher |
University of Szeged |
| series |
Electronic Journal of Qualitative Theory of Differential Equations |
| issn |
1417-3875 1417-3875 |
| publishDate |
1998-01-01 |
| description |
We prove the existence and uniqueness of a global solution of a damped quasilinear hyperbolic equation. Key point to our proof is the use of the Yosida approximation. Furthermore, we apply a method based on a specific integral inequality to prove that the solution decays exponentially to zero when the time t goes to infinity. |
| url |
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=12 |
| work_keys_str_mv |
AT maassila asymptoticbehaviorofsolutionstoaquasilinearhyperbolicequationwithnonlineardamping |
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1721303948503023616 |