Global existence for a wave equation on \(\mathbb R^N\) (Q932395)
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scientific article; zbMATH DE number 5299843
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global existence for a wave equation on \(\mathbb R^N\) |
scientific article; zbMATH DE number 5299843 |
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Global existence for a wave equation on \(\mathbb R^N\) (English)
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11 July 2008
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The paper refers to the Cauchy problem for a nonlocal quasilinear wave equation of Kirchhoff type with weak dissipative term. A discussion on existence and uniqueness of the local weak solution is done. Next, energy and potential functional are associated to the problem and decay estimates for the energy are shown. Under some special assumptions, existence of a unique global solution together with decay estimates are proved.
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quasilinear hyperbolic equations
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dissipation
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blow-up
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Kirchhoff strings
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generalized Sobolev spaces
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concavity method
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energy functional
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potential functional
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0.9457587
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0.94289637
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0.9365798
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0.9324497
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0.9322134
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0.9313338
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0.9309515
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0.9299072
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