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Wave Equation with Logarithmic Nonlinearities in Kirchhoff Type |
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PP: 2163-2172 |
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doi:10.18576/amis/100618
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Author(s) |
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Khaled Zennir,
Salah Boulaaras,
Mohamed Haiour,
Mohsin Bayoud,
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Abstract |
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| In this paper, we study a viscoelastic wave equations of the Kirchhoff type
u′′ −f (x)
M(kÑxuk22
)Dxu−
Z t
0
g(t −s)Dxu(s)ds
= auln |u|k (1)
defined in any spaces dimension. It is well known that from a class of nonlinearities the logarithmic nonlinearity is distinguished by
several interesting physical properties. We use weighted spaces to establish the long-time behavior of solution of (1). Furthermore,
under convenient hypotheses on g and the initial data, the local-in-time existence of solution is established. |
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