Wave-Front Tracking for the Equations of Non-Isentropic Gas Dynamics -- Basic Lemmas --
Wave-Front Tracking for the Equations of Non-Isentropic Gas Dynamics -- Basic Lemmas --
复制标题
非等熵气体动力学方程的波前跟踪 -- 基本引理 --
DOI：
10.1007/s40306-013-0030-3
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发表时间：
2013
影响因子：
0.5
通讯作者：
F. Asakura
中科院分区：
文献类型：
--
作者：
Itoh;Hiromichi; Khludnev;A. M.; Rudoy;E. M.; Tani;Atusi;F. Asakura
在随机选择及其替代波前跟踪方法中，近似解是通过精确地或近似地求解依赖于时间的某个有限跳跃点集的每个邻域中的黎曼问题来构造的。为了得到时间上的整体BV解，必须对近似解的总变差进行先验估计，粗略地说，这就是构成Riemann问题解的波的振幅之和。由于振幅可以通过相邻波的相互作用而增加，因此关键点是在单个黎曼解中通过入射波的振幅来估计出射波的振幅，本文的目的是详细描述多方气体动力学方程的Riemann问题，并完整地证明局部相互作用估计所依据的基本引理是基于。尽管除了引理4.2和5.1之外，所有的引理都在T. P. Liu（印第安纳州大学数学杂志26：147-177，1977），这篇论文很难，尽管它很重要，但即使在今天也没有很好地理解。为了完整起见，本说明包括局部相互作用估计的证明。
In the random choice and its alternative wave-front tracking methods, approximate solutions are constructed by solving exactly or approximately the Riemann problem in each neighborhood of a certain finite set of jump points depending on the time. In order to obtain global in time BV solutions, one has to get a priori estimates for the total variation inxat the timetof approximate solutions, which is, roughly speaking, the summation of amplitudes of waves attconstituting the solutions to the Riemann problems. Since amplitudes may increase through the interaction of neighboring waves, the crucial point is to estimate the amplitudes of outgoing waves by those of incoming waves in a single Riemann solution, which is called thelocal interaction estimates.The aim of this note is to provide a detailed description of the Riemann problem to the equations of polytropic gas dynamics and a complete proof of the basic lemmas on which the local interaction estimates are based. Although all of them, except for Lemmas 4.2 and 5.1, are presented in T.-P. Liu (Indiana Univ. Math. J. 26:147–177, 1977), that paper is difficult and not well understood even at the present day in spite of its importance. For the sake of completeness, this note includes proofs of the local interaction estimates.