BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Svetlana Mukhina DTSTART:20230607T162000Z DTEND:20230607T180000Z DTSTAMP:20260423T010236Z UID:GDEq/89 DESCRIPTION:Title: Co ntact vs symplectic geometry\nby Svetlana Mukhina as part of Geometry of differential equations seminar\n\nLecture held in room 303 of the Indep endent University of Moscow.\n\nAbstract\nThe report will show how some sy mplectic Monge-Ampère type equations can be solved by applying contact tr ansformations to them.\n\nAs is known\, symplectic Monge-Ampère equations with two independent variables are locally symplectic equivalent to linea r equations with constant coefficients if and only if the corresponding Ni jenhuis bracket is zero (the Lychagin-Rubtsov theorem). Necessary and suff icient conditions for the contact equivalence of the general (not necessar ily symplectic) Monge-Ampère linear equations were found by Kushner.\n\nU sing these results\, we consider the problem of constructing exact solutio ns to some equations arising in filtration theory. We will consider a mode l of unsteady displacement of oil by a solution of active reagents. This m odel describes the process of oil extraction from hard-to-recover deposits . This model is described by a hyperbolic system of partial differential e quations of the first order of the Jacobi type. Unknown functions are the water saturation and concentration of reagents in an aqueous solution\, an d independent variables are time and linear coordinate.\n\nWith the help o f symplectic and contact transformations\, it is possible to reduce the mo del equations to a linear wave equation. The exact solution of this system is obtained and the Cauchy problem is solved.\n LOCATION:https://researchseminars.org/talk/GDEq/89/ END:VEVENT END:VCALENDAR