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DTSTAMP:20260211T135224
DTSTART;TZID=America/Detroit:20260225T160000
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SUMMARY:Workshop / Seminar:Probability and Analysis Seminar: Finite time singularities in the Landau equation with very hard potentials
DESCRIPTION:The Landau equation\, introduced by Lev Landau in 1936\, is one of the central equations in kinetic theory. We consider the Landau equation with very hard potentials $\gamma \in (\sqrt{3}\,2]$\, which is known to admit global smooth solutions for homogeneous data. Inspired by hydrodynamic limits from kinetic equations to fluid equations\, we construct smooth\, strictly positive initial data that develop a finite-time singularity by lifting imploding singularities from the compressible Euler equations. In self‑similar variables\, the solution becomes asymptotically hydrodynamic—the distribution function converges to a local Maxwellian\, while the hydrodynamic fields develop an asymptotically self‑similar implosion whose profile coincides with a smooth imploding profile of the compressible Euler equations.  To our knowledge\, this provides the first example of a collisional kinetic model which is globally well-posed in the homogeneous setting\, but admits finite time singularities for inhomogeneous data.\n \nThis is joint work with Jacob Bedrossian (UCLA)\, Maria Gualdani (UT Austin)\, Sehyun Ji (UChicago)\, Vlad Vicol (NYU)\, and Jincheng Yang (JHU).
UID:145282-21897003@events.umich.edu
URL:https://events.umich.edu/event/145282
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4088
CONTACT:
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DTSTAMP:20260223T020145
DTSTART;TZID=America/Detroit:20260225T160000
DTEND;TZID=America/Detroit:20260225T170000
SUMMARY:Workshop / Seminar:Student AIM Seminar: A Beginner’s introduction to optimal control theory
DESCRIPTION:In this talk I describe the basic deterministic control problem and how to solve it using the method of the adjoint function. The method is motivated through examination of the problem’s structure and properties its solutions would exhibit. Hopefully by the end of this talk you’ll know what an adjoint function is\, be able to solve basic optimal control problems\, and have an idea of when solutions exist.
UID:145805-21897837@events.umich.edu
URL:https://events.umich.edu/event/145805
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Applied Mathematics
LOCATION:East Hall - 3088
CONTACT:
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