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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

Tatsien Li 1, and  Libin Wang 2,

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.
Keywords: global classical solution, Quasilinear hyperbolic system, mixed initial-boundary value problem, weak linear degeneracy..
Mathematics Subject Classification: 35L50, 35Q72, 74K0.
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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