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

Baoxiang Wang

doi:10.3934/dcds.1999.5.753

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1999, Volume 5, Issue 4: 753-763. Doi: 10.3934/dcds.1999.5.753

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

Baoxiang Wang^1,

1.
Department of Mathematics, Hebei University, Baoding, 071002

Received: October 31, 1998

Revised: May 31, 1999

Published: September 1999

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Abstract

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.

Keywords:

Klein-gordon equations,
scattering of solutions.

Mathematics Subject Classification: 35L70.

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

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