TY - JOUR
T1 - Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems
AU - Shumin Li 
JO - Journal of Partial Differential Equations
VL - 1
SP - 46
EP - 68
PY - 2002
DA - 2002/02
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5440.html
KW - Quasilinear hyperbolic system
KW - matching condition
KW - life-span
KW - weak linear degeneracy
AB -  In this paper, we consider Cauchy problem for general first order inho- mogeneous 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.