# On the Initial Boundary-Value Problem in the Kinetic Theory of Hard Particles II: Non-uniqueness

@article{Wilkinson2018OnTI, title={On the Initial Boundary-Value Problem in the Kinetic Theory of Hard Particles II: Non-uniqueness}, author={Mark Wilkinson}, journal={arXiv: Classical Analysis and ODEs}, year={2018} }

In the first of two papers, we study the initial boundary-value problem that underlies the theory of the Boltzmann equation for general non-spherical hard particles. In this work, for two congruent ellipses and for a large class of associated boundary conditions, we identify initial conditions for which there do not exist local-in-time weak solutions of Newton's equations of motion. To our knowledge, this is the first time the necessity of rolling in the energy-conserving dynamics of strictly…

## One Citation

### On the Non-uniqueness of Physical Scattering for Hard Non-spherical Particles

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We prove the existence of uncountably-many physical scattering maps for non-spherical hard particles which, when used to construct global-in-time weak solutions of Newton’s equations of motion,…

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