Phase Space Analysis of Partial Differential Equations

# Global existence of small solutions for nonlinear symmetric hyperbolic systems

speaker: Kunihiko Kajitani (University of Tsukuba)

abstract: In this paper we shall investigate the decay of solutions of the Cauchy problem for first order symmetric hyperbolic system with variable coefficients and obtain the existence of global small amplitude solution of quasilinear symmetric hyperbolic systems. In order to derive decay estimates of solutions we make use of the spectrul theory for first order symmetric hyperbolic systems, in particular, the integral representation of wave operator amang constant operators and operators with variable coefficients and L\infty and L1 boundedness of wave operators. Furthermore applying the decay estimates we show small anplitude global solutions of the Cauchy problem for nonlinear symmetric hyperbolic systems and obtain the nonlinear scattering.

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