In this paper, we consider Cauchy problem for general first order inhomogeneous quasilinear strictly hyperbolic systems. Under the matching condition, we first give an estimate on inhomogeneous terms. By this estimate, we obtain the asymptotic behaviour for the life-span of C1 solutions with "slowly" decaying and small initial data and prove that the formation of singularity is due to the envelope of characteristics of the same family.
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