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Seminários do IMPA

Sistemas Dinâmicos

Título |
Solutions of differential equations from a non-Lipschitz singularity |

Expositor |
Alexei A. Mailybaev
IMPA |

Data |
Quarta-feira, 24 de janeiro de 2018, 15:30 |

Local |
Sala 236. |

Resumo |

We consider a system of ordinary differential equations with an isolated non-Lipschitz singularity. First, I will describe the motivation of using such a system as a toy-model for the phenomenon of finite-time blowup in partial differential equations describing, in particular, turbulence. Solutions passing through the non-Lipschitz singular point in finite time become strongly non-unique: there are infinite number of solutions from a singular point. So our focus will be the definition of the regularization procedure (analogous to the inviscid limit in fluid dynamics) that provides a natural selection mechanism. We will see that the selection principle reduces to the classification of attractors in a properly defined renormalized dynamical system.