Special Session 97: Analysis and control of nonlinear partial differential equation evolution systems
Contents
We will present qualitative and numerical results on a partial differential equation (PDE)
system which models a certain fluid-structure dynamics. The wellposedness of this PDE model is
established by means of constructing for it a nonstandard semigroup generator representation;
this representation is essentially accomplished by an appropriate elimination of the pressure. Wellposedness of this fluid-structure dynamics is attained
through a certain nonstandard variational (inf-sup) formulation. Subsequently we show how
our constructive proof of wellposedness naturally gives rise to a certain mixed
finite element
method for numerically approximating solutions of this fluid-structure dynamics.