BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:A. A. Shlapunov (SibFU\, Krasnoyarsk\, Russia) DTSTART:20241128T110000Z DTEND:20241128T120000Z DTSTAMP:20260423T005820Z UID:mmandim/83 DESCRIPTION:Title: Maxwell's and Stokes' operators associated with elliptic differential com plexes\nby A. A. Shlapunov (SibFU\, Krasnoyarsk\, Russia) as part of M athematical models and integration methods\n\n\nAbstract\nWe propose a reg ular method for generating consistent systems of partial differential equa tions (PDEs) that describe a wide class of models in natural sciences. Suc h systems appear within typical constructions of the Homological Algebra a s complexes of differential operators describing compatibility conditions for overdetermined PDEs. Additional assumptions on the ellipticity/paramet er-dependent ellipticity of the differential complexes provide a wide ran ge of elliptic\, parabolic and hyperbolic operators. In particular\, most equations related to modern Mathematical Physics are generated by the de R ham complex of differentials on exterior differential forms. These include s the equations based on elliptic Laplace and Lam\\'e type operators\; the parabolic heat and mass transfer equations\; the Euler type and Navier-St okes type equations in Hydrodynamics\; the hyperbolic wave equation and th e Maxwell equations in Electrodynamics\; the Klein-Gordon equation in Rela tivistic Quantum Mechanics\; and so on. The advantage of our approach is t hat this generation method covers a broad class of generating systems\, es pecially in high dimensions\, due to different underlying algebraic struct ures than the conventional ones.\n\nThis is joint work with V. L. Mironov and A. N. Polkovnikov.\n LOCATION:https://researchseminars.org/talk/mmandim/83/ END:VEVENT END:VCALENDAR