Existence theory and L super()pestimates for the solution of nonlinear viscous wave equation

Existence theory and L super()pestimates for the solution of nonlinear viscous wave equation

In this paper, we consider the global existence of the Cauchy problem for the nonlinear viscous wave equation. We apply the approach introduced in Li and Chen (1989) [15] and get the global existence theory directly by using the decaying properties of the solution. Such properties are obtained by lo...

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Veröffentlicht in:Nonlinear analysis: real world applications 2010-10, Vol.11 (5), p.4404-4414
Hauptverfasser: Deng, Shijin, Wang, Weike, Zhao, Hualei
Format: Artikel
Sprache:eng
Schlagworte:
Cauchy problem
Decay
Decomposition
Estimates
Green's functions
Interpolation
Nonlinearity
Wave equations
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Zusammenfassung:In this paper, we consider the global existence of the Cauchy problem for the nonlinear viscous wave equation. We apply the approach introduced in Li and Chen (1989) [15] and get the global existence theory directly by using the decaying properties of the solution. Such properties are obtained by long wave-short wave decomposition, Green's function method and energy estimates. Finally, we show the L super()pestimates for the solution by interpolation lemma.
ISSN:1468-1218
DOI:10.1016/j.nonrwa.2010.05.024