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Scattering theory in the energy space for a class of non-linear wave equations (1989)

Ginibre, J. ; Velo, G.

Springer

Communications in mathematical physics 123 (1989), S. 535-573

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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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