Abstract
We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain \(\Omega \). 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.
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Acknowledgements
MK and PvM gratefully acknowledge support from JSPS KAKENHI Grant Number 20KK0058. PvM gratefully acknowledges support from JSPS KAKENHI Grant Number 20K14358.
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Kimura, M., van Meurs, P. & Yang, Z.X. Particle Dynamics with Elastic Collision at the Boundary: Existence and Partial Uniqueness of Solutions. Acta Appl Math 174, 5 (2021). https://doi.org/10.1007/s10440-021-00423-4
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DOI: https://doi.org/10.1007/s10440-021-00423-4