BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Filippo Riva (University of Pavia) DTSTART:20211011T134000Z DTEND:20211011T151000Z DTSTAMP:20260405T174815Z UID:NSCM/38 DESCRIPTION:Title: In ertial Balanced Viscosity solutions to rate-independent systems\nby Fi lippo Riva (University of Pavia) as part of Nečas Seminar on Continuum Me chanics\n\n\nAbstract\nRate-independent evolutions frequently occur in mec hanics when \nthe problem\nunder consideration presents such small rate-de pendent effects\, as \ninertia or viscosity\, that can be neglected. If th e driving potential \nenergy is nonconvex any (reasonable) solution necess arily exhibits \ntime-discontinuities. To describe the behaviour of the ju mps\, in the \nlast decades the notions of Energetic and Balanced Viscosit y solutions \nhave been developed\, the latter as a refinement of the form er. While for \nEnergetic solutions the cost at jumps is described only in terms of the \nrate-independent dissipation potential\, in the case of Ba lanced \nViscosity solutions it arises from a suitable coupling between th is \ndissipation potential and a smaller and smaller viscosity potential\, \nwhich is reminiscent of an original presence of viscous damping.\nIn th is talk we present a novel notion of solution to rate-independent \nsystem s\, named Inertial Balanced Viscosity (IBV) solution\, which in \naddition takes into account small inertial effects. Differently from the \npreviou s cases\, now the jump cost turns out to be rate-dependent. In \nfinite di mension\, we show how IBV solutions can be obtained as a \nvanishing inert ia and viscosity limit of dynamic evolutions\, and we \nintroduce a multis cale Minimizing Movements algorithm which can be used \nto build such solu tions.\nThis is a joint work with G. Scilla and F. Solombrino.\n LOCATION:https://researchseminars.org/talk/NSCM/38/ END:VEVENT END:VCALENDAR