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On space-time means and everywhere defined scattering operators for nonlinear Klein-Gordon equations. (English) Zbl 0524.35084


MSC:

35P25 Scattering theory for PDEs
47A40 Scattering theory of linear operators
35Q99 Partial differential equations of mathematical physics and other areas of application
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References:

[1] Brenner, P.: On weightedL p -L p?-estimates for the Klein-Gordon equation, Report 1982-25. Department of Mathematics, Chalmers University of Technology and the University of G?teborg, Sweden
[2] Brenner, P.: Scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations, Report 1982-09 (revised). Department of Mathematics, Chalmers University of Technology and the University of G?teborg, Sweden
[3] Glassey, R., Tsusumi, M.: On uniqueness of weak solutions to semilinear wave equations. Comm. Partial Differential Equations7, 153-195 (1982) · Zbl 0503.35059
[4] Marshall, B.: Mixed norm estimates for the Klein-Gordon equation. In: Proceedings of a Conference on Harmonic Analysis (Chicago 1981)
[5] Pecher, H.: Nonlinear Small Data Scattering for the Wave and Klein-Gordon Equation. Math. Z.185, 261-270 (1984) · Zbl 0538.35063
[6] Segal, I.E.: Space-time decay for solutions of wave equations, Advances in Math.22, 302-311 (1976) · Zbl 0344.35058
[7] Strauss, W.A.: In Invariant Wave Equations (Erice 1977). Lecture Notes in Physics73, pp. 197-249. Berlin-Heidelberg-New York: Springer 1978
[8] Strauss, W.A.: Non-linear scattering theory at low energy. J. Funct. Anal.41, 110-133 (1981) · Zbl 0466.47006
[9] Strauss, W.A.: Mathematical aspects of classical nonlinear field equations. In: Nonlinear problems in theoretical physics (Jaca, Huesca 1978). Lecture Notes in Physics98, pp. 124-149. Berlin-Heidelberg-New York: Springer 1979
[10] Strauss, W.A.: Everywhere defined wave operators. In: Nonlinear Evolution Equations, pp. 85-102. New York: Academic Press 1978 · Zbl 0466.47005
[11] Strichartz, R.S.: Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J.44, 705-714 (1977) · Zbl 0372.35001
[12] Thomas, P.: A restriction theorem for the Fourier transform. Bull. Amer. Math. Soc.81, 477-478 (1975) · Zbl 0298.42011
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