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Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data
Author(s) -
Shao ZhiQiang
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2930
Subject(s) - mathematics , norm (philosophy) , bounded function , minkowski space , smoothness , nonlinear system , mathematical analysis , hyperbolic partial differential equation , degenerate energy levels , partial differential equation , pure mathematics , mathematical physics , physics , quantum mechanics , political science , law
We investigate the existence of a global classical solution to the Goursat problem for linearly degenerate quasilinear hyperbolic systems. As the result in [A. Bressan, Contractive metrics for nonlinear hyperbolic systems, Indiana Univ. Math. J. 37 (1988) 409–421] suggests that one may achieve global smoothness even if the C 1 norm of the initial data is large, we prove that, if the C 1 norm of the boundary data is bounded but possibly large, and the BV norm of the boundary data is sufficiently small, then the solution remains C 1 globally in time. Applications include the equation of time‐like extremal surfaces in Minkowski space R 1 + (1 + n ) and the one‐dimensional Chaplygin gas equations. Copyright © 2013 John Wiley & Sons, Ltd.
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