# American Institute of Mathematical Sciences

January  2005, 12(1): 59-78. doi: 10.3934/dcds.2005.12.59

## Global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems

 1 School of Mathematical Sciences, Fudan University, Shanghai 200433, China 2 Institute of Mathematics, Fudan University, Shanghai 200433

Received  June 2003 Revised  July 2004 Published  December 2004

In this paper, we consider the mixed initial-boundary value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in a half-unbounded domain {$(t,x)|\ t\geq 0,x\geq 0$}. Under the assumption that the positive eigenvalues are weakly linearly degenerate, we obtain the global existence and uniqueness of $C^1$ solution with small and decaying initial data. Some applications are given for the system of the planar motion of an elastic string.
Citation: Tatsien Li, Libin Wang. Global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems. Discrete & Continuous Dynamical Systems, 2005, 12 (1) : 59-78. doi: 10.3934/dcds.2005.12.59
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