BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexei Kushner DTSTART:20230426T162000Z DTEND:20230426T180000Z DTSTAMP:20260423T010249Z UID:GDEq/87 DESCRIPTION:Title: Fi nite-dimensional dynamics of systems of evolutionary differential equation s with many spatial variables\nby Alexei Kushner as part of Geometry o f differential equations seminar\n\n\nAbstract\nThe main ideas of the theo ry of finite-dimensional dynamics were formulated in the 2000s in the work s of B.S. Kruglikov\, V.V. Lychagin and O.V. Lychagina. These papers also found finite-dimensional dynamics of the Kolmogorov-Petrovsky-Piskunov and Korteweg-de Vries equations. This theory is a natural development of the theory of dynamical systems. Finite-dimensional dynamics make it possible to find families of solutions depending on a finite number of parameters a mong all solutions of evolutionary differential equations. Namely\, finite -dimensional submanifolds are constructed in the space of smooth functions that are invariant under the flow given by the evolution equation. This r emoves the question of the existence of solutions\, since such submanifold s consist of solutions to ordinary differential equations\, and\, moreover \, gives a constructive method for finding them. Note that finite-dimensio nal dynamics can exist for equations that do not have symmetries. The talk will present the results obtained by us for systems of evolutionary equat ions\, including those with many spatial variables.\n LOCATION:https://researchseminars.org/talk/GDEq/87/ END:VEVENT END:VCALENDAR