标题： 一种带有变分广义 Chaplygin 气体的 2x2 Keyfitz-Kranzer 型平衡系统的分析 显示英文标题

标题： An Analysis of a 2x2 Keyfitz-Kranzer Type Balance System with Varying Generalized Chaplygin Gas

摘要： 我们考虑一个具有变化的广义 Chaplygin 气体的 Keyfitz-Kranzer 型两个平衡定律系统，该系统表现出负压，并且是时间函数和密度的幂的倒数的乘积。 Chaplygin 气体是一种流体，旨在适应早期宇宙和晚期宇宙膨胀的测量结果，同时遵循压力-密度-时间关系。 我们提供了对非自相似 Riemann 解的解释和描述，包括非经典奇异解。 我们还发现，由于对时间的直接依赖，允许经典和非经典奇异解组合的区域发生变化，因此 Riemann 解在不同的时间区间内可能有不同的解。 我们的发现通过局部 Lax-Friederichs 格式进行了数值验证。 显示英文摘要

摘要： We consider a system of two balance laws of Keyfitz-Kranzer type with varying generalized Chaplygin gas, which exhibits negative pressure and is a product of a function of time and the inverse of a power of the density. The Chaplygin gas is a fluid designed to accommodate measurements for the early universe and late-time universal expansion while obeying the pressure-density-time relation. We produce an explanation and description of the non-self-similar Riemann solutions, including the non-classical singular solutions. We also find that due to a direct dependence on time, a change in the regions allowing for combinations of classical and non-classical singular solutions occurs, therefore a Riemann solution can have different solutions over several time intervals. Our findings are confirmed numerically using the local Lax-Friederichs scheme.