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GLOBAL WEAKLY DISCONTINUOUS SOLUTIONS TO THE MIXED INITIAL–BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

ZHI-QIANG SHAO

Department of Mathematics, Fuzhou University, Fuzhou 350002, China

https://doi.org/10.1142/S0218202509003735Cited by:3 (Source: Crossref)

Abstract

In this paper, we consider the mixed initial–boundary value problem for first-order quasilinear hyperbolic systems with general nonlinear boundary conditions in the half space {(t, x) | t ≥ 0, x ≥ 0}. Based on the fundamental local existence results and global-in-time a priori estimates, we prove the global existence of a unique weakly discontinuous solution u = u(t, x) with small and decaying initial data, provided that each characteristic with positive velocity is weakly linearly degenerate. Some applications to quasilinear hyperbolic systems arising in physics and other disciplines, particularly to the system describing the motion of the relativistic closed string in the Minkowski space R¹⁺ⁿ, are also given.

Keywords:

AMSC: 35L45, 35L50, 35Q72

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