GLOBAL WEAKLY DISCONTINUOUS SOLUTIONS TO THE MIXED INITIAL–BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS
2009 ◽
Vol 19
(07)
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pp. 1099-1138
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Keyword(s):
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.
2011 ◽
Vol 78
(1)
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pp. 1-31
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2009 ◽
Vol 360
(2)
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pp. 398-411
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2007 ◽
Vol 22
(2)
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pp. 181-200
2003 ◽
Vol 52
(2)
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pp. 573-583
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2005 ◽
Vol 12
(1)
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pp. 59-78
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