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2004 Scattering states for the nonlinear wave equation with small data
Tokio Matsuyama, Minoru Tanaka
Adv. Differential Equations 9(7-8): 721-744 (2004).


We investigate the energy nondecay and existence of scattering states for solutions to the initial-boundary-value problem for the nonlinear wave equation in exterior domains. When the space dimension is odd, the domain meets no geometrical condition. Otherwise, we assume that the obstacle is convex. For odd-dimensional general domains, taking into account the effective dissipation in trapping regions, we can derive the existence of scattering states. In particular, we can obtain also an $L^2$ bound of solutions. The method in deriving the energy nondecay is to utilize Huyghens' principle. For even-dimensional domains outside the convex obstacle, the asymptotics stated in the odd-dimensional case are also valid.


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Tokio Matsuyama. Minoru Tanaka. "Scattering states for the nonlinear wave equation with small data." Adv. Differential Equations 9 (7-8) 721 - 744, 2004.


Published: 2004
First available in Project Euclid: 18 December 2012

zbMATH: 1102.35072
MathSciNet: MR2100393

Primary: 35L70
Secondary: 35L20, 35P25

Rights: Copyright © 2004 Khayyam Publishing, Inc.


Vol.9 • No. 7-8 • 2004
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