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Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems of diagonal form with large BV data

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  • We investigate the existence of a global classical solution to the Goursat problem for linearly degenerate quasilinear hyperbolic systems of diagonal form. As the result in [A. Bressan, Contractive metrics for nonlinear hyperbolic systems, Indiana Univ. Math. J. 37 (1988) 409-421] suggests that one may achieve global smoothness even if the $C^1$ norm of the initial data is large, we prove that, if the $C^1$ norm and the BV norm of the boundary data are bounded but possibly large, then the solution remains $C^1$ globally in time. Applications include the equation of time-like extremal surfaces in Minkowski space $R^{1+(1+n)}$ and the one-dimensional Chaplygin gas equations.
    Mathematics Subject Classification: Primary: 35L45, 35L60; Secondary: 35Q40.

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