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2006 Small-data scattering for nonlinear waves of critical decay in two space dimensions
Paschalis Karageorgis, Kimitoshi Tsutaya
Differential Integral Equations 19(6): 601-626 (2006).

Abstract

Consider the nonlinear wave equation with zero mass in two space dimensions. When it comes to the associated Cauchy problem with small initial data, the known existence results are already sharp; those require the data to decay at a rate $k\geq k_c$, where $k_c$ is a critical decay rate that depends on the order of the nonlinearity. However, the known scattering results treat only the supercritical case $k>k_c$. In this paper, we prove the existence of the scattering operator for the full optimal range $k\geq k_c$.

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Paschalis Karageorgis. Kimitoshi Tsutaya. "Small-data scattering for nonlinear waves of critical decay in two space dimensions." Differential Integral Equations 19 (6) 601 - 626, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35274
MathSciNet: MR2234716

Subjects:
Primary: 35L70
Secondary: 35B40 , 35P25

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 6 • 2006
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