asymptotic behavior for a nondissipative and nonlinear system of the kirchhoff viscoelastic type
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ID: 257847
2012
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Abstract
A wave equation of the Kirchhoff type with several nonlinearities is stabilized by a viscoelastic damping. We consider the case of nonconstant (and unbounded) coefficients. This is a nondissipative case, and as a consequence the nonlinear terms cannot be estimated in the usual manner by the initial energy. We suggest a way to get around this difficulty. It is proved that if the solution enters a certain region, which we determine, then it will be attracted exponentially by the equilibrium.
| Reference Key |
tatar2012journalasymptotic
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|---|---|
| Authors | ;Nasser-Eddine Tatar |
| Journal | Chemico-biological interactions |
| Year | 2012 |
| DOI |
10.1155/2012/936140
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| URL | |
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