论文标题
减震型的光谱稳定性夸张的守护定律系统
Spectral stability of shock profiles for hyperbolically regularized systems of conservation laws
论文作者
论文摘要
我们报告了一个证明，在自然假设下，如果休克幅度足够小，则将其视为杂智性行驶波解决方案被视为杂智性行动波解决方案，即夸张的环保系统在光谱上是稳定的。这意味着与$λ\ subset \ subset \ mathbb {c} $的关联的evans函数$ \ mathcal {e}：λ\ rightarrow \ mathbb {c} $ $ \ mathbb {h}^+\ equiv \ {κ\ in \ mathbb {c}：\ text {re} \，κ\ geq 0 \} $，只有一个零，即简单的零零，即$ 0 $。结果类似于在[FS02]和[PZ04]中获得的寄生规范性保护定律系统中获得的结果，并且在[PZ04]，[MZ09]，[UED09]中明显扩展了对双曲线弛豫系统的发现。
We report a proof that under natural assumptions shock profiles viewed as heteroclinic travelling wave solutions to a hyperbolically regularized system of conservation laws are spectrally stable, if the shock amplitude is sufficiently small. This means that an associated Evans function $\mathcal{E}:Λ\rightarrow\mathbb{C}$ with $Λ\subset\mathbb{C}$ an open superset of the closed right half plane $\mathbb{H}^+\equiv\{κ\in\mathbb{C}:\text{Re}\,κ\geq 0\}$, has only one zero, namely a simple zero at $0$. The result is analogous to the one obtained in [FS02] and [PZ04] for parabolically regularized systems of conservation laws, and also distinctly extends findings on hyperbolic relaxation systems in [PZ04], [MZ09], [Ued09] .
