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Asymptotic behaviour of global classical solutions of diagonalizable quasilinear hyperbolic systems
Author(s) -
Liu Jianli,
Zhou Yi
Publication year - 2006
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.797
Subject(s) - mathematics , diagonalizable matrix , minkowski space , bounded function , degenerate energy levels , infinity , norm (philosophy) , mathematical analysis , hyperbolic space , pure mathematics , eigenvalues and eigenvectors , mathematical physics , symmetric matrix , physics , quantum mechanics , political science , law
This paper is concerned with the asymptotic behaviour of global classical solutions of diagonalizable quasilinear hyperbolic systems with linearly degenerate characteristic fields. Based on the existence results of global classical solutions, we prove that when t tends to infinity, the solution approaches a combination of C 1 travelling wave solutions, provided that L 1 ∩ L ∞ norm of the initial data as well as its derivative are bounded. Application is given for the time‐like extremal surface in Minkowski space. Copyright © 2006 John Wiley & Sons, Ltd.