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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

机译:一阶拟线性双曲系统单边混合初边值问题的行波解的存在性和稳定性

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摘要

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 (c) 2014 John Wiley & Sons, Ltd.
机译:当系统的一个特征线性退化时,在适当的边界条件下,我们得到了存在于单边混合初边值问题的相应特征轨迹上的行波解的存在。当系统线性退化时,通过引入半全局归一化坐标,我们推导了相关的波分解公式,以证明与所有左,右特征轨迹相对应的行波解的稳定性。最后,对于与其他向右特征轨迹相对应的行波解,一些示例表明了它们可能的不稳定性。版权所有(c)2014 John Wiley&Sons,Ltd.

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