Relative Morse indices, Fredholm indices, and group velocities
Relative Morse indices, Fredholm indices, and group velocities
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相对莫尔斯指数、Fredholm 指数和群速度
DOI：
10.3934/dcds.2008.20.139
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发表时间：
2007
影响因子：
1.1
通讯作者：
A. Scheel
中科院分区：
文献类型：
--
作者：
Bjorn Sandstede;A. Scheel
我们讨论关于行波和调制波的圆柱域上偏微分方程线性化的 Fredholm 性质。我们表明，每个此类线性化的 Fredholm 指数由相对莫尔斯指数给出，该相对莫尔斯指数仅取决于渐近系数。概述了几种有助于使用空间特征值的交叉数计算相对莫尔斯指数的策略，并将结果应用于证明在添加小局部时间周期源项后双曲守恒定律中存在小粘性冲击波。
We discuss Fredholm properties of the linearization of partial differential equations on cylindrical domains about travelling and modulated waves. We show that the Fredholm index of each such linearization is given by a relative Morse index which depends only on the asymptotic coefficients. Several strategies are outlined that help to compute relative Morse indices using crossing numbers of spatial eigenvalues, and the results are applied to prove the existence of small viscous shock waves in hyperbolic conservation laws upon adding small localized time-periodic source terms.