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In this article, we investigate the global existence and asymptotic behavior of classical solutions to Goursat problem for diagonalizable quasilinear hyperbolic system. Under the assumptions that system is strictly hyperbolic and linearly degenerate, we obtain the global existence and uniqueness of C 1 solutions with the bounded L 1 ∩ L ∞ norm of the boundary data as well as their derivatives. Based on the existence result, we can prove that when t tends to in nity, the solutions approach a combination of piece-wised C 1 traveling wave solutions. As the important example, we apply the results to the chaplygin gas system. © 2012 Liu and Pan; licensee Springer.

Global existence and asymptotic behavior of classical solutions to Goursat problem for diagonalizable quasilinear hyperbolic system