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Existence and stability of traveling wave solutions to one‐sided mixed initial‐boundary value problem for first‐order quasilinear hyperbolic systems
Author(s) -
Liu Cunming,
Qu Peng
Publication year - 2014
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.3166
Subject(s) - mathematics , traveling wave , degenerate energy levels , mathematical analysis , boundary value problem , stability (learning theory) , initial value problem , boundary (topology) , instability , order (exchange) , trajectory , physics , mechanics , finance , quantum mechanics , astronomy , machine learning , computer science , economics
When one characteristic of the system is linearly degenerate, under suitable boundary conditions, we get the existence of traveling wave solutions located on the corresponding characteristic trajectory to the one‐sided mixed initial‐boundary value problem. When the system is linearly degenerate, by introducing the semi‐global normalized coordinates, we derive the related formulas of wave decomposition to prove the stability of traveling wave solutions corresponding to all leftward and the rightmost characteristic trajectories. Finally, for the traveling wave solutions corresponding to other rightward characteristic trajectories, some examples show their possible instability. Copyright © 2014 John Wiley & Sons, Ltd.