BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bob Pego (CMU) DTSTART:20260602T200000Z DTEND:20260602T210000Z DTSTAMP:20260604T053257Z UID:UCLAAnalysisSeminar/255 DESCRIPTION:Title: Analysis of the adhesion model and reconstruction in cosmolo gy\nby Bob Pego (CMU) as part of UCLA analysis and PDE seminar\n\nLect ure held in MS 6627.\n\nAbstract\nIn cosmology\, a basic explanation of th e observed concentration of mass\nin singular structures is provided by th e Zeldovich approximation\, which\ntakes the form of free-streaming flow f or perturbations of a uniform\nEinstein-de Sitter universe in co-moving co ordinates. The adhesion\nmodel suppresses multi-streaming by introducing v iscosity. We study\nmass flow in this model by analysis of Lagrangian adve ction in the\nzero-viscosity limit. Under mild conditions\, we show that a unique\nlimiting Lagrangian semi-flow exists. Limiting particle paths sti ck\ntogether after collision and are characterized uniquely by a\ndifferen tial inclusion. The absolutely continuous part of the mass\nmeasure satisf ies a Monge-Ampère equation related to convexification of\nthe free-strea ming velocity potential.\n\nThe use of Monge-Ampère equations and optimal transport theory for the\nreconstruction of inverse Lagrangian maps in co smology was introduced in\nwork of Brenier and Frisch et al (2003). We sho w that the singular part\nof the mass measure can differ from the Alexandr ov solution to the\nMonge-Ampère equation\, however\, when flows along si ngular structures\nmerge\, as shown by analysis of a 2D Riemann problem. I n a neighborhood\nof merging singular structures in our examples\, we show that\nreconstruction yielding a monotone Lagrangian map cannot be exact a .e.\,\neven off of the singularities themselves.\n LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/255/ END:VEVENT END:VCALENDAR