AI 中文总结
本文针对带时变阻尼与通量的非自治朗缪尔等温线色谱型系统，分析其波相互作用与黎曼解稳定性，构造扰动黎曼问题的全局弱解并通过数值实验验证结果，属该方向首次研究。
AI 中文摘要
本文研究带有随时间变化的阻尼和通量的朗缪尔等温线非自治色谱型系统的波相互作用与黎曼解稳定性。该系统模拟具有随时间变化的饱和容量n(t)的双组分色谱分离，形成非自治双曲平衡律系统。我们考虑分段常数初始数据在x=±ε处存在两个跳跃间断的扰动黎曼问题，通过分析所有可能的经典（激波、稀疏波、接触间断）和非经典（δ激波）波相互作用构造全局弱解。我们证明当ε→0时，扰动黎曼问题的解在Radon测度空间中收敛到对应黎曼问题的解，建立了黎曼解在初始数据小扰动下的稳定性。据我们所知，这是首次对具有随时间变化系数的非自治色谱型系统进行波相互作用与稳定性分析。采用Lax-Friedrichs型格式的数值实验展示了波相互作用结构、特定时刻的剖面以及ε→0时的渐近收敛性。
英文摘要
We investigate the wave interactions and stability of Riemann solutions for a nonautonomous chromatography-type system of Langmuir isotherm with time-dependent damping and flux. The system models two-component chromatographic separation with a time-dependent saturation capacity $n(t)$, leading to a nonautonomous hyperbolic system of balance laws. We consider a perturbed Riemann problem with piecewise constant initial data having two jump discontinuities at $x = \pmε$, and construct the global weak solution by analyzing all possible wave interactions, both classical (shock waves, rarefaction waves, contact discontinuities) and nonclassical (delta shock waves). We prove that as $ε\to 0$, the solution of the perturbed Riemann problem converges to the solution of the corresponding Riemann problem in the space of Radon measures, establishing the stability of Riemann solutions under small perturbations of the initial data. To the best of our knowledge, this is the first instance of wave interaction and stability analysis for a nonautonomous chromatography-type system with time-dependent coefficients. Numerical experiments using a Lax-Friedrichs type scheme illustrate the wave interaction structure, the profiles at selected times, and the asymptotic convergence as $ε\to 0$.
Comments51 pages
