alle ore 14,30 presso Sala Conferenze “F. Tricerri" del Dipartimento di Matematica e Informatica "U. DINI"
Il Prof. Pavel Krejci
(Academy of Sciences of the Czech Republic)
terrà una conferenza dal titolo:
"MAGNETIC FLUID FLOW WITH HYSTERESIS"
abstract: We propose to describe plane flow of a conducting fluid in a thin layer between two ferromagnetic plates. The model leads to a coupled system of two PDEs in 2D, namely the scalar Maxwell equation for the magnetic field which is assumed perpendicular to the plane of motion, and the vector Navier-Stokes equation for the fluid velocity. Both equations contain hysteresis terms which are due to the ferromagnetic reaction of the surrounding medium. To ensure thermodynamic consistency of the model, hysteresis is expressed in terms of the Preisach model. The main result includes existence and uniqueness of a strong solution for regular data as long as the magnetic field stays in the convexity domain of the Preisach operator (joint work with M. Eleuteri and J. Kopfova).
alle ore 15,30 presso Sala Conferenze “F. Tricerri" del Dipartimento di Matematica e Informatica "U. DINI"
Il Prof. Virginia Aostiniani
(Mathematical Institute, University of Oxford)
terrà una conferenza dal titolo:
"A GEOMETRIC APPROACH TO SOME OVERDETERMINED PROBLEMS IN POTENTIAL THEORY"
abstract: In this talk, we present a method which we have developed in order to deal with some overdetermined elliptic boundary value problems. We illustrate this approach for a classical problem arising in potential
theory in the exterior domain Rn n: the one which denes the electrostatic potential u. The main idea is to reformulate the problem in terms of a metric g which is conformally equivalent to the at metric by a factor dened as a suitable power of u. This reformulation allows us to identify a natural boundary condition on the mean curvature of @ under which the original problem becomes overdetermined and which ensures the splitting of the metric g as a Riemannian product. By the conformally atness of g, we can then deduce that is a ball and that u is rotationally symmetric.