Stability and Asymptotic Behavior of Periodic Traveling Wave Solutions of Viscous Conservation Laws in Several Dimensions
Stability and Asymptotic Behavior of Periodic Traveling Wave Solutions of Viscous Conservation Laws in Several Dimensions
复制标题
多维粘性守恒定律周期行波解的稳定性和渐近行为
DOI：
10.1007/s00205-009-0229-6
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发表时间：
2008
影响因子：
2.5
通讯作者：
K. Zumbrun
中科院分区：
文献类型：
--
作者：
M. Oh;K. Zumbrun
在自然谱稳定性假设下，我们确定了粘性守恒律系统多维平面周期波线性化解算子的Lp估计，给出了线性化的L1 → Lp → Lp稳定性和非线性L1 → Lp → Lp稳定性以及L2-渐近性$$和$${d\geqq 3}$$。这种行为通常相当复杂，包括对流（即波浪状）和扩散效应。
Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem, we determine sharp Lp estimates on the linearized solution operator about a multidimensional planar periodic wave of a system of conservation laws with viscosity, yielding linearized L1 ∩ Lp → Lp stability for all $${p \geqq 2}$$ and dimensions $${d \geqq 1}$$ and nonlinear L1 ∩ Hs → Lp ∩ Hs stability and L2-asymptotic behavior for $${p\geqq 2}$$ and $${d\geqq 3}$$ . The behavior can in general be rather complicated, involving both convective (that is, wave-like) and diffusive effects.