General Decay of Energy for a Class of Integro-Differential Equation with Nonlinear Damping
In this paper, a class of non-linear Integro-differential equations is considered in a bounded domain Ω with a smooth boundary ∂Ω as follows: utt + M(kD muk 2 2)(−∆)mu(t) + Z t 0 g(t − s)(−∆)mu(s)ds + |ut| α−1 ut = |u| p−1 u. The asymptotic behavior of solutions is discussed by some c...
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| Format: | Article |
| Language: | English |
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Islamic Azad University
2012-06-01
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| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/164/86 |
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doaj-8b77371aee0d4e3f99fa6f6d1063bca22020-11-25T03:40:49ZengIslamic Azad UniversityJournal of Mathematical Extension1735-82991735-82992012-06-01625164General Decay of Energy for a Class of Integro-Differential Equation with Nonlinear DampingE. Hesameddini0Y. Khalili1Shiraz University of TechnologyShiraz University of TechnologyIn this paper, a class of non-linear Integro-differential equations is considered in a bounded domain Ω with a smooth boundary ∂Ω as follows: utt + M(kD muk 2 2)(−∆)mu(t) + Z t 0 g(t − s)(−∆)mu(s)ds + |ut| α−1 ut = |u| p−1 u. The asymptotic behavior of solutions is discussed by some conditions on g. Decay estimates of the energy function of solutions are also given.http://ijmex.com/index.php/ijmex/article/view/164/86 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
E. Hesameddini Y. Khalili |
| spellingShingle |
E. Hesameddini Y. Khalili General Decay of Energy for a Class of Integro-Differential Equation with Nonlinear Damping Journal of Mathematical Extension |
| author_facet |
E. Hesameddini Y. Khalili |
| author_sort |
E. Hesameddini |
| title |
General Decay of Energy for a Class of Integro-Differential Equation with Nonlinear Damping |
| title_short |
General Decay of Energy for a Class of Integro-Differential Equation with Nonlinear Damping |
| title_full |
General Decay of Energy for a Class of Integro-Differential Equation with Nonlinear Damping |
| title_fullStr |
General Decay of Energy for a Class of Integro-Differential Equation with Nonlinear Damping |
| title_full_unstemmed |
General Decay of Energy for a Class of Integro-Differential Equation with Nonlinear Damping |
| title_sort |
general decay of energy for a class of integro-differential equation with nonlinear damping |
| publisher |
Islamic Azad University |
| series |
Journal of Mathematical Extension |
| issn |
1735-8299 1735-8299 |
| publishDate |
2012-06-01 |
| description |
In this paper, a class of non-linear Integro-differential equations
is considered in a bounded domain Ω with a smooth boundary ∂Ω
as follows:
utt + M(kD
muk
2
2)(−∆)mu(t)
+
Z t
0
g(t − s)(−∆)mu(s)ds + |ut|
α−1
ut = |u|
p−1
u.
The asymptotic behavior of solutions is discussed by some conditions
on g. Decay estimates of the energy function of solutions are also given. |
| url |
http://ijmex.com/index.php/ijmex/article/view/164/86 |
| work_keys_str_mv |
AT ehesameddini generaldecayofenergyforaclassofintegrodifferentialequationwithnonlineardamping AT ykhalili generaldecayofenergyforaclassofintegrodifferentialequationwithnonlineardamping |
| _version_ |
1724532744453619712 |