论文标题
双曲线平衡系统的Riemann冲击的指数渐近稳定性
Exponential asymptotic stability of Riemann shocks of hyperbolic systems of balance laws
论文作者
论文摘要
对于严格的平衡法律系统的严格熵Riemann休克解决方案，我们证明指数频谱稳定性意味着大的渐近轨道稳定性。作为一项准备，我们还证明了初始值和初始边界价值问题的恒定解决方案的结果相似，这似乎是新的一般性。主要的关键技术成分包括变量的非线性变化，从而提供了具有耗散性边界条件的低碳kawashima型结构，并且在高频式方案中具有耗散的边界条件，并明确地识别了线性化演化的最奇异部分，这两者都是从单纯的频谱假设中推导的。
For strictly entropic Riemann shock solutions of strictly hyperbolic systems of balance laws, we prove that exponential spectral stability implies large-time asymptotic orbital stability. As a preparation, we also prove similar results for constant solutions of initial value and initial boundary value problems, that seem to be new in this generality. Main key technical ingredients include the design of a nonlinear change of variables providing a hypocoercive Kawashima-type structure with dissipative boundary conditions in the high-frequency regime and the explicit identification of most singular parts of the linearized evolution, both being deduced from the mere spectral assumption.
