October  1999, 5(4): 753-763. doi: 10.3934/dcds.1999.5.753

Scattering of solutions for critical and subcritical nonlinear Klein-Gordon equations in $H^s$

1. 

Department of Mathematics, Hebei University, Baoding, 071002, China

Received  November 1998 Revised  June 1999 Published  July 1999

We study the scattering theory for nonlinear Klein-Gordon equations $u_{t t} + (m^2-\Delta)u = f_1(u) + f_2(u)$. We show that the scattering operator carries a band in $H^s \times H^{s-1}$ into $H^s \times H^{s-1}$ for all $s\in [1/2,\ \infty)$ if $f_i(u)\ (i = 1,\ 2)$ have $H^s$-critical or $H^s$-subcritical powers.
Citation: Baoxiang Wang. Scattering of solutions for critical and subcritical nonlinear Klein-Gordon equations in $H^s$. Discrete & Continuous Dynamical Systems, 1999, 5 (4) : 753-763. doi: 10.3934/dcds.1999.5.753
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