Nonlinear scattering for a system of one dimensional nonlinear Klein-Gordon equations

HAYASHI, Nakao; PAVEL, Naumkin I.

Hokkaido Math. J., Tome 37 (2008) no. 4, p. 647-667 / Harvested from Project Euclid

Résumé

We consider a system of nonlinear Klein-Gordon equations in one space dimension with quadratic nonlinearities (∂_t²+∂_x²+ m_j²)u_j = N_j(∂u), ¶ j = 1, . . . , l. We show the existence of solutions in an analytic function space. When the nonlinearity satisfies a strong null condition introduced by Georgiev we prove the global existence and obtain the large time asymptotic behavior of small solutions.

Publié le : 2008-11-15
Classification: systems of Klein Gordon equations, scattering problem, one dimension, 35L70, 35L15

@article{1249046362,
     author = {HAYASHI, Nakao and PAVEL, Naumkin I.},
     title = {Nonlinear scattering for a system of one dimensional nonlinear Klein-Gordon equations},
     journal = {Hokkaido Math. J.},
     volume = {37},
     number = {4},
     year = {2008},
     pages = { 647-667},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1249046362}
}

HAYASHI, Nakao; PAVEL, Naumkin I. Nonlinear scattering for a system of one dimensional nonlinear Klein-Gordon equations. Hokkaido Math. J., Tome 37 (2008) no. 4, pp.  647-667. http://gdmltest.u-ga.fr/item/1249046362/