Global existence of classical solutions to the Cauchy problem on a semi-bounded initial axis for quasilinear hyperbolic systems Original Research Article

In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Under the assumption that the leftmost (resp. rightmost) eigenvalue is weakly linearly degenerate, we obtain the global existence and uniqueness of C1 solution with small and decaying initial data.