22 may 2003

Abstract.

date and place: Thursday, May 22, 4.30 PM at Centro De Giorgi

speaker: Alexander PLAKHOV (Universidade de Aveiro, Portugal)

title: Newton's problem of minimal resistance: The case of multiple collisions

Abstract: A body moves through a homogeneous medium consisting of non-interacting particles at rest. When colliding with the body surface, the particles reflect elastically. It is required to find the shape of the body with minimal resistance to the medium. This problem was first considered by I. Newton in a class of convex and radially symmetric bodies; in the last decade, various classes of bodies have also been studied, provided each particle interacts with the body at most once. We consider the case where multiple collisions of the particles with the body are allowed. It is shown, in particular, that resistance of a body can be made arbitrarily small by a small deformation of the body near its boundary. The two-dimensional version of Newton's problem is also considered.