Global existence, scattering, rigidity and inverse scattering for some quasilinear hyperbolic systems

Abstract

Abstract We study the Cauchy problem of multidimensional quasilinear hyperbolic systems of diagonal form without self-interaction. In both L 1 {L^{1}} and L ∞ {L^{\infty}} frameworks, we will first show the global existence of classical solutions with small initial data, and then prove that the global solution will scatter to free linear waves and study the rigidity aspect of the scattering problem. We also show the inverse scattering result: The scattering field can determine the global solution uniquely, in the L 1 {L^{1}} framework.