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Théorie de la diffusion pour des équations semi linéaires. (Scattering theory for semilinear equations). (French) Zbl 0627.35078

Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1985, No. 2, 1-6 (1985).
The author presents an up-to-date survey of results on scattering theory for the semilinear Schrödinger equation (1) \(iu_ t=-\Delta u+f(u)\) and the semilinear Klein-Gordon equation (2) \(u_{tt}-\Delta u+u+f(u)=0\). In recent years, the author in collaboration with G. Velo has made significant contributions to the subject. Most of their most recent joint work is described in this survey. A quite complete list of references on (1) and (2) is given.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35G20 Nonlinear higher-order PDEs
35P25 Scattering theory for PDEs
Full Text: Numdam EuDML