×

Scattering problem for a system of nonlinear Klein-Gordon equations related to Dirac-Klein-Gordon equations. (English) Zbl 1167.35427

Summary: We prove the existence of a scattering operator for a system of nonlinear Klein-Gordon equations related to Dirac-Klein-Gordon equations in three space dimensions.

MSC:

35P25 Scattering theory for PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35B45 A priori estimates in context of PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bachelot, A., Problème de Cauchy global pour des systèmes de Dirac-Klein-Gordon, Ann. Inst. H. Poincaré, 48, 387-422 (1988) · Zbl 0672.35071
[2] Georgiev, V., Global solution of the system of wave and Klein-Gordon equations, Math. Z., 203, 683-698 (1990) · Zbl 0671.35052
[3] Georgiev, V., Decay estimates for the Klein-Gordon equation, Commun. Partial Differential Equations, 17, 1111-1139 (1992) · Zbl 0767.35068
[4] N. Hayashi, P.I. Naumkin, Scattering operator for the nonlinear Klein-Gordon equations, Commun. Contemp. Math. (in press); N. Hayashi, P.I. Naumkin, Scattering operator for the nonlinear Klein-Gordon equations, Commun. Contemp. Math. (in press) · Zbl 1182.35198
[5] Hayashi, N.; Naumkin, P. I., Scattering operator for the nonlinear Klein-Gordon equations in higher space dimensions, J. Differential Equations, 244, 188-199 (2008) · Zbl 1136.35079
[6] Hayashi, N.; Naumkin, P. I.; Edy Wibowo, Ratno Bagus, Nonlinear scattering for a system of nonlinear Klein-Gordon equations, J. Math. Phys., 49, 103501 (2008) · Zbl 1152.81467
[7] Hörmander, L., Lectures on Nonlinear Hyperbolic Differential Equations (1997), Springer-Verlag: Springer-Verlag Berlin, New York, Heidelberg · Zbl 0881.35001
[8] Klainerman, S., Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, Commun. Pure Appl. Math., 38, 631-641 (1985) · Zbl 0597.35100
[9] Marshall, B.; Strauss, W.; Wainger, S., \(L^p - L^q\) estimates for the Klein-Gordon equation, J. Math. Pures Appl., 59, 417-440 (1980) · Zbl 0457.47040
[10] Yajima, K., Existence of solutions for Schrödinger evolution equations, Comm. Math. Phys., 110, 415-426 (1987) · Zbl 0638.35036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.