标题： 对具有特殊状态方程的气体动力学系统的对称性分析和新的部分不变解 显示英文标题

标题： Symmetry analysis and new partially invariant solutions for the gas dynamics system with a special equation of state

摘要： 本文是对气体动力学系统对称性分析的贡献，延续了Ovsyannikov（1994）提出的“podmodeli”（子模型）程序。 我们考虑特殊情况方程，规定压力为熵和密度的任意函数之和。 这样的系统具有12维的对称李代数。 本研究推进了其四维子代数的研究，继续了Siraeva（2024）开始的工作。 对于Siraeva（2014）中一个最优列表中的大量之前未被考虑的非相似四维子代数，我们计算了一个完整的生成不变量集合。 对于其中一个子代数，我们构造了一个部分对称约化系统。 我们显式求解这个约化系统（子模型）。 这导致了原系统的新的显式解族。 我们分析了这些解的轨迹。 此外，我们将本文中考虑的每个子代数与其同构类进行匹配，为未来对约化系统的层次结构的研究奠定了基础。 显示英文摘要

摘要： This paper is a contribution to the symmetry analysis of the gas dynamics system in the vein of the ''podmodeli'' (submodels) program outlined by Ovsyannikov (1994). We consider the case of the special state equation, prescribing pressure to be the sum of entropy and an arbitrary function of density. Such a system has a 12-dimensional symmetry Lie algebra. This work advances the study of its four-dimensional subalgebras, continuing the work started in Siraeva (2024). For a large subset of not previously considered, non-similar four-dimensional subalgebras from an optimal list in Siraeva (2014), we compute a complete set of generating invariants. For one of the subalgebras, we construct a partially symmetry-reduced system. We explicitly solve this reduced system (submodel). This leads to new families of explicit solutions of the original system. We analyze the trajectories of these solutions. Additionally, we match each of the subalgebras considered in this paper with its isomorphism class, planting a seed for future study of the hierarchy of the reduced systems.