In　this　paper,　we　investigate　the　asymptotic　behavior　of　global　classical　solutions　to　the　mixed　initial-boundary　value　problem　with　large　bounded　total　variation　(BV)　data　for　linearly　degenerate　quasilinear　hyperbolic　systems　of　diagonal　form　with　general　non-linear　boundary　conditions　in　the　half　space　{(t,　x)vertical　bar　t　＞=　0,　x　＞=　0}.　Based　on　the　existence　result　on　the　global　classical　solution,　we　prove　that　when　t　tends　to　the　infinity,　the　solution　approaches　a　combination　of　C-1　travelling　wave　solutions,　provided　that　the　C-1　norm　and　the　BV　norm　of　the　initial　and　boundary　data　are　bounded　but　possibly　large.　Applications　include　the　1D　Born-Infeld　system　arising　in　the　string　theory　and　high　energy　physics.