Global Existence of Classical Solutions to the Cauchy Problem on a Semi-bounded Initial Axis for Inhomogeneous Quaslinear Hyperbolic Systems

Abstract

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.