Abstract
We study the asymptotic behaviour in time of the solutions and the theory of scattering in the energy space for the non-linear wave equation
in ℝn,n≧3. We prove the existence of the wave operators, asymptotic completeness for small initial data and, forn≧4, asymptotic completeness for arbitrarily large data. The assumptions onf cover the case wheref behaves slightly better than a single powerp=1+4/(n−2), both near zero and at infinity (see (1.5), (1.6) and (1.8)).
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Communicated by A. Jaffe
Laboratoire associé au Centre National de la Recherche Scientifique
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Ginibre, J., Velo, G. Scattering theory in the energy space for a class of non-linear wave equations. Commun.Math. Phys. 123, 535–573 (1989). https://doi.org/10.1007/BF01218585
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DOI: https://doi.org/10.1007/BF01218585