Erratum to: Asymptotic estimates and stability analysis of Kuramoto-Sivashinsky type models
Erratum to: Asymptotic estimates and stability analysis of Kuramoto-Sivashinsky type models
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勘误表：Kuramoto-Sivashinsky 型模型的渐近估计和稳定性分析
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
A. Stefanov
中科院分区：
文献类型：
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作者：
M. Stanislavova;A. Stefanov
必然有一个不稳定的特征值（即具有负实部的特征值）。在我们对这一主张的论证中，我们正确地验证了一个必要条件，但这不是一个充分条件。事实上，结果证明，（1）存在稳定和不稳定的定态解，例如参见[1]。因此，命题2中关于线性不稳定性的陈述（即第二部分）是无效的。我们对这一错误感到遗憾，并感谢我们的同事M。约翰逊和K.让我们注意到这件事在我们与约翰逊和尊布伦的讨论中出现的另一个问题是我们强加给算子L的谱条件（A）的不可信性。也就是说，我们要求，
necessarily has an unstable eigenvalue (that is an eigenvalue with negative real-part). In our justification for this claim, we have correctly verified a necessary condition, which is however not a sufficient one. In fact, it turned out that there are stable as well as unstable stationary solutions to (1), see for example [1]. Thus, the statement of linear instability (namely part 2) in Proposition 2 is invalid. We regret this error, and we are grateful to our colleagues M. Johnson and K. Zumbrun for bringing this to our attention. Another issue that came up during our discussions with Johnson and Zumbrun is the implausibility of the spectral condition (A) that we have imposed on the operator L. Namely, we have required that