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.

中文翻译：

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一些多维拟线性双曲系统的全局存在性和渐近行为

摘要 对于无自相互作用的多维拟线性双曲系统的柯西问题，我们证明了小初始数据下经典解的全局存在性。我们还证明，随着时间趋于无穷大，全局解会收敛到线性化系统的解，并且收敛速度也是确定的。