AI 中文总结
该研究针对结构化Keyfitz-Kranzer守恒律系统，通过施加结构条件构建解的分类框架，依据特征值演化划分函数类别并判定有限时间爆破情况，最终将Riemann问题解分为经典解与含delta激波或真空态的解。
AI 中文摘要
形如$U_t + (Φ(U) U)_x =0$、$U: R_t\times R_x\rightarrow R^n$（$n\neq 2$）且$Φ(U) = ϕ(r, Θ): R^n\rightarrow R$（其中$r = |U|$，$Θ= U/|U|\n S^{n-1}$）的守恒律系统的若干应用，通过施加结构条件得到，从而为依赖$ϕ(U)$形式的解提供分类框架。通过指定某一特征值的演化，我们可将满足该演化的这类函数$ϕ$划分为依赖标量场$z=rK(Θ)$（其中$K: S^{n-1}\rightarrow R$）或依赖向量场$Θ$的类别，并找出解的振幅可能在有限时间内爆破的情况。由此，对应Riemann问题的解可分为经典解以及涉及delta激波和/或真空态的解。
英文摘要
Several applications for systems of conservation laws of the form $U_t + (Φ(U) U)_x =0$, $U: R_t\times R_x\rightarrow R^n$ , $n\geq 2$, with $Φ(U) = ϕ(r, Θ): R^n\rightarrow R$, $r = |U|$, and $Θ= U/|U|\in S^{n-1}$, are obtained by imposing structural conditions to provide a classification framework for solutions dependent on the form of $ϕ(U)$. By prescribing the evolution of a particular eigenvalue, we can categorize classes of such functions, $ϕ$, for which this evolution is met, into depending on either a scalar field $z=rK(Θ)$, where $K: S^{n-1}\rightarrow R$, or on the vector field $Θ$, and find for which the amplitude of solutions may blow up in finite time. As a consequence, solutions to the corresponding Riemann problems can be divided into those with are classical and those which involve delta-shocks and/or vacuum states.
Comments36 pages
Journal refJournal of Elasticity (2026)
DOI：10.1007/s10659-026-10220-5
