Global existence and asymptotic behavior for some multidimensional quasilinear hyperbolic systems

Abstract

For the Cauchy problem of multidimensional quasilinear hyperbolic systems of diagonal form without self-interaction, we show the global existence of classical solutions with small initial data. We also prove that the global solution will converge to a solution of the linearized system as time tends to infinity, and the convergence rate is also determined.