Unique solutions to hyperbolic conservation laws with a strictly convex entropy
Unique solutions to hyperbolic conservation laws with a strictly convex entropy
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具有严格凸熵的双曲守恒定律的独特解
DOI：
10.1016/j.jde.2024.01.005
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发表时间：
2023
影响因子：
2.4
通讯作者：
G. Guerra
中科院分区：
文献类型：
--
作者：
A. Bressan;G. Guerra
考虑严格双曲n×n守恒律系统，其中每个特征场要么是真正的非线性的，要么是线性退化的。在这个标准设置下，众所周知，存在定义在具有小总变分的函数域上的弱解的Lipschitz半群。如果系统具有严格的凸熵，我们给出了一个简短的证明，证明了在半群区域内取值的每一个熵弱解都与半群轨迹重合。结果表明，在存在严格凸熵的情况下，可以去掉以前用来实现唯一性的“驯化变分”或“驯化振荡”的假设。
Consider a strictly hyperbolic n× n system of conservation laws, where each characteristic field is either genuinely nonlinear or linearly degenerate. In this standard setting, it is well known that there exists a Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation. If the system admits a strictly convex entropy, we give a short proof that every entropy weak solution taking values within the domain of the semigroup coincides with a semigroup trajectory. The result shows that the assumptions of “Tame Variation” or “Tame Oscillation”, previously used to achieve uniqueness, can be removed in the presence of a strictly convex entropy.
双曲守恒定律数值解的后验误差估计
影响因子：
2.5
作者：
Bressan, Alberto;Chiri, Maria Teresa;Shen, Wen
通讯作者：
Shen, Wen