lle ore 14,30 presso Sala Conferenze “F. Tricerri" del Dipartimento di Matematica e Informatica "U. DINI"
Il Prof. George Avalos
(University of Nebraska-Lincoln, U.S.A.)
terrà una conferenza dal titolo:
"AN APPLIED FUNCTIONAL ANALYSIS FOR A CERTAIN FLUID-STRUCTURE INTERACTIVE PDE"
abstract: In this talk we will present qualitative and numerical results for a partial differential equation (PDE) system which models a fluid-structure PDE of longstanding interest within the mathematical literature. The coupled PDE model under discussion involves a Stokes or Navier-Stokes system, which evolves on a three dimensional domain, interacting with a fourth order plate equation which evolves on a flat portion of said fluid domain. Among other technical difficuties we note that, inasmuch as the fluid velocity does not vanish on all of the boundary, the associated pressure variable cannot be eliminated via the classic Leray Projector. We will discuss how wellposedness of this fluid-structure dynamics is eventually attained via a certain variational "inf-sup" (or Babuska-Brezzi) formulation. Subsequently, we will show how our constructive proof of wellposedness naturally gives rise to a finite element method for numerically approximating solutions to the fluid-structure dynamics. Time permitting, we will also discuss a result of backward uniqueness for this PDE system. (This is joint work with Tom Clark.)