Applied Mathematics Colloquium: Dr. Pelin Geredeli

Title: On the qualitative properties of a Compressible Flow-Elastic Solid Interaction 

Abstract: We consider a compressible flow structure interaction (FSI) PDE system which is linearized about some reference rest state. The deformable interface is under the effect of an ambient field generated by the underlying and unbounded material derivative term which further contributes to the non-dissipativity of the FSI system. We show that, on an appropriate subspace, only one dimension less than the entire finite energy space, the FSI system is wellposed, and is moreover associated with a continuous semigroup which is uniformly bounded in time. Also, we analyze the long time dynamics in the sense of asymptotic (strong) stability in this appropriate invariant subspace. In order to obtain these qualitative results, our approach involves establishing maximal dissipativity of the semigroup generator for the given FSI system and proving the pointwise resolvent condition introduced by Chill and Tomilov for the stability of bounded semigroups.