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Corpus ID: 119683510

"Life after death" in ordinary differential equations with a non-Lipschitz singularity

@article{Drivas2018LifeAD,
title={"Life after death" in ordinary differential equations with a non-Lipschitz singularity},
author={Theodore D. Drivas and A. Mailybaev},
journal={arXiv: Classical Analysis and ODEs},
year={2018}
}

We consider a class of ordinary differential equations in $d$-dimensions featuring a non-Lipschitz singularity at the origin. Solutions of such systems exist globally and are unique up until the first time they hit the origin, $t = t_b$, which we term `blowup'. However, infinitely many solutions may exist for longer times. To study continuation past blowup, we introduce physically motivated regularizations: they consist of smoothing the vector field in a $\nu$--ball around the origin and then… Expand