论文标题
对流反应扩散方程的均匀渐近稳定性，在侵入性限制的对流限制中
Uniform asymptotic stability for convection-reaction-diffusion equations in the inviscid limit towards Riemann shocks
论文作者
论文摘要
目前的贡献证明了标量平衡定律的稳定riemann冲击的粘性正规化的渐近轨道稳定性，相对于粘度/扩散参数$ε$均匀。从某种意义上说，均匀性是稳定性陈述均匀的，并且相应的多尺度$ε$依赖性拓扑均减少到经典的$ W^{1，\ infty} $ - 仅限于从冲击位置支撑的功能时。主要困难包括，统一性排除了抛物线正规化来关闭规律性估计，全球时间分析在空间上也是多尺度的，这是由于非平凡的慢速部分与快速冲击较高的部分共存，这使得限制平稳的光谱问题（在快速变量中）没有光谱差距，并且没有均匀的稳定性和均匀的阶段，并且需要一个均匀的设计。特别是，我们的分析构建了一个阶段，该阶段在兰金·霍尼奥特条件所规定的双曲线冲击位置与仅通过逐步逐步逐步逐步逐步划出非定位$ 0 $ mmode而引起的非均匀转移，就像反应 - 延伸方程的前沿的经典稳定性分析一样。
The present contribution proves the asymptotic orbital stability of viscous regularizations of stable Riemann shocks of scalar balance laws, uniformly with respect to the viscosity/diffusion parameter $ε$. The uniformity is understood in the sense that all constants involved in the stability statements are uniform and that the corresponding multiscale $ε$-dependent topology reduces to the classical $W^{1,\infty}$-topology when restricted to functions supported away from the shock location. Main difficulties include that uniformity precludes any use of parabolic regularization to close regularity estimates, that the global-in-time analysis is also spatially multiscale due to the coexistence of nontrivial slow parts with fast shock-layer parts, that the limiting smooth spectral problem (in fast variables) has no spectral gap and that uniformity requires a very precise and unusual design of the phase shift encoding orbital stability. In particular, our analysis builds a phase that somehow interpolates between the hyperbolic shock location prescribed by the Rankine-Hugoniot conditions and the non-uniform shift arising merely from phasing out the non-decaying $0$-mode, as in the classical stability analysis for fronts of reaction-diffusion equations.
