Ecole Doctorale 184

Positivity preserving property for some models in plate theory

Par Giulio Romani

Consider a thin plate of some uniform material, an external force which pushes it upwards and let's suppose that the plate cannot move on its boundary : are we sure that it will bend upwards in every point, or instead, there will be some portions of it going downwards? During this talk, two different possible ways to model this situation are presented, the so called “hinged plate” and “clamped plate”, which rely on some fourth-order linear PDEs. They will lead us to different phenomena, according also to the shape of our plate, some of them natural and some of them counter-intuitive.