论文标题
边界处具有弹性碰撞的粒子动力学：解决方案的存在和部分独特性
Particle dynamics with elastic collision at the boundary: existence and partial uniqueness of solutions
论文作者
论文摘要
我们考虑限制在有界的，可能是非convex域$ω$的点粒子的动力学。与边界的碰撞描述为纯粹的弹性碰撞。这将粒子动力学的描述变成了不连续的右侧的二阶ODES耦合系统。本文的主要贡献是为该粒子系统开发精确的解决方案概念，并证明解决方案的存在。在此证明中，我们通过基于Yosida近似的辅助问题中的极限来构建解决方案。除了存在解决方案外，我们还建立了部分独特性定理，并通过反例显示了解决方案的唯一性一般不能保持。
We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain $Ω$. Collisions with the boundary are described as purely elastic collisions. This turns the description of the particle dynamics into a coupled system of second order ODEs with discontinuous right-hand side. The main contribution of this paper is to develop a precise solution concept for this particle system, and to prove existence of solutions. In this proof we construct a solution by passing to the limit in an auxiliary problem based on the Yosida approximation. In addition to existence of solutions, we establish a partial uniqueness theorem, and show by means of a counterexample that uniqueness of solutions cannot hold in general.
