初始数据位于其中一个黎曼不变量水平集的弹性动力学系统的波相互作用
Wave Interaction For A System In Elastodynamics With Initial Data Lying On The Level Set Of One Of The Riemann Invariants
AI总结：
本文针对弹性波传播的严格双曲非守恒系统，在初始数据位于黎曼不变量水平集的情形下得到波相互作用解的显式公式，突破了传统分析需初始数据满足小性条件的限制，为全局解构造提供支撑。
摘要：
本文研究了弹性波传播方程组系统中，源自两个不同点的黎曼问题的波的相互作用。该系统由关于$(u,σ)$的两个方程组成，其中$u$为速度，$σ$为应力，系统是严格双曲且非守恒的。波相互作用研究是利用Glimm格式等近似方法构造有界变差函数空间中初始数据的全局解的最重要步骤之一。这相当于构造初始数据包含三个状态$(u_L, σ_L)$、$(u_m, σ_m)$和$(u_R, σ_R)$的解。通常这类分析是针对处于某个固定状态的小邻域内的状态开展的。本文中，当数据位于黎曼不变量的水平集时，我们得到了该系统解的显式公式。本工作的特色在于我们未对初始数据施加小性条件。
英文摘要：
This paper is concerned with the study of interaction of waves originating from the Riemann problem centred at two different points for a system of equations modelling propagation of elastic waves. The system consists of two equations for $(u,σ)$, where, u is the velocity and $σ$ is the stress and is strictly hyperbolic and nonconservative. Study of interaction of waves is one of the most important steps in the construction of global solution with initial data in the space of functions of bounded variation using approximation procedure like the Glimm's scheme. This amounts to constructing a solution with initial data consisting of three states $(u_L, σ_L), (u_m, σ_m),$ and $(u_R, σ_R)$. Usually this analysis is done for the states which are in a small neighbourhood of a fixed state. Here we get explicit formula for the solution of the system when the data lies in the level sets of Riemann invariants. The speciality of the work is that we donot assume smallness conditions on the initial data.
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