TY - JOUR
T1 - Global Existence of Classical Solutions to the Cauchy Problem on a Semi-bounded Initial Axis for Inhomogeneous Quaslinear Hyperbolic Systems
AU - Weiwei Han 
JO - Journal of Partial Differential Equations
VL - 3
SP - 273
EP - 288
PY - 2007
DA - 2007/08
SN - 20
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5308.html
KW - Inhomogeneous quasilinear hyperbolic system
KW - Cauchy problem
KW - global classical solution
KW - weak linear degeneracy
KW - matching condition
AB -  In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost (resp. leftmost) eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C¹ solution with small and decaying initial data.