Global existence of classical solutions to the mixed initial–boundary value problem for quasilinear hyperbolic systems of diagonal form with large BV data

AbstractIn this paper, we investigate the mixed initial–boundary value problem with large BV data for linearly degenerate quasilinear hyperbolic systems of diagonal form with general nonlinear boundary conditions in the half space {(t,x)|t⩾0,x⩾0}. 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 C1 norm of the initial data is large, we prove that, if the C1 norm and the BV norm of the initial and boundary data are bounded but possibly large, then the solution remains C1 globally in time and possesses uniformly bounded total variation in x for all t⩾0. As an application, we apply the result to the system describing the motion of relativistic closed strings in the Minkowski space R1+n