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

Tatsien Li; Libin Wang

doi:10.3934/dcds.2005.12.59

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2005, Volume 12, Issue 1: 59-78. Doi: 10.3934/dcds.2005.12.59

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

Tatsien Li^1, and
Libin Wang²

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

Received: May 31, 2003

Revised: June 30, 2004

Published: March 2005

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Abstract

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.

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Mathematics Subject Classification: 35L50, 35Q72, 74K05.

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