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首页> 外文期刊>ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees >Wave interactions and stability of the Riemann solutions for a scalar conservation law with a discontinuous flux function
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Wave interactions and stability of the Riemann solutions for a scalar conservation law with a discontinuous flux function

机译：具有不连续通量函数的标量守恒律的Riemann解的波相互作用和稳定性

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摘要

This paper is devoted to studying the interactions of elementary waves for a model of a scalar conservation law with a flux function involving discontinuous coefficients. In order to cover all the situations completely, we take the initial data as three piecewise constant states and the middle region is regarded as the perturbed region with small distance. It is proved that the Riemann solutions are stable under the local small perturbations of the Riemann initial data by letting the perturbed parameter tend to zero. The proof is based on the detailed analysis of the interactions of stationary wave discontinuities with shock waves and rarefaction waves. Moreover, the global structures and large time asymptotic behaviors of the solutions are constructed and analyzed case by case.
机译：本文致力于研究具有包含不连续系数的通量函数的标量守恒定律模型的基本波相互作用。为了完全覆盖所有情况，我们将初始数据取为三个分段恒定状态，中间区域视为距离较小的扰动区域。通过使被摄动的参数趋于零，证明了黎曼解在黎曼初始数据的局部小扰动下是稳定的。该证明是基于对平稳波不连续性与冲击波和稀疏波相互作用的详细分析得出的。此外，构造并解的解决方案的全局结构和大时间渐近行为。

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