ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
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 $$\square \varphi + f(\varphi ) = 0$$ in ℝ n ,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)).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01218585
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