Global Existence of Classical Solution with Small Initial Total Variation for Quasilinear Linearly Degenerate Hyperbolic Systems

In this paper, the author proves the global existence of classical solution to the Cauchy problem with slowly decaying initial data with small initial total variation for general first order quasilinear linearly degenerate hyperbolic systems. This generalizes the corresponding result of A.Bressan for initial data with compact support.