Mathematics and Statistics Colloquium (Sep 25)
Speaker: Justin Webster (University of Maryland, Baltimore County)
Time: September 25, 4-5pm
Location: IES 110
Title: Stability and Periodicity in Linear Systems
Abstract: Time-periodicity arises in physical systems as (i) responses to forcing (blood flow in human tissues) or (ii) as self-excitations (aeroelastic flutter). In this talk, we consider an idealized fluid-structure interaction: a coupled heat-wave system, with a time-periodic external force. For undamped systems, the phenomenon of resonance can occur. For heat-type systems it cannot, and the existence and uniqueness theory of periodic solutions is well-established. Yet the case of coupled heat-wave systems is indeterminate, and periodicity is not characterized by the abstract theory of dissipative systems.
We will provide a construction of unique periodic solutions for this heat-wave system. A priori estimates will be achieved through boundary control methods, introducing geometric constraints into the problem. Thus, for certain classes of spatial domains, unique periodic solutions will be obtained from temporally smooth forcing, eliminating the possibility of resonance. We call attention to the "gap" between smoothness of the forcing and resulting solutions, and it remains open whether the geometric and regularity constraints are technical, or necessary to circumvent the emergence of resonance.
Speaker: Justin Webster (University of Maryland, Baltimore County)
Time: September 25, 4-5pm
Location: IES 110
Title: Stability and Periodicity in Linear Systems
Abstract: Time-periodicity arises in physical systems as (i) responses to forcing (blood flow in human tissues) or (ii) as self-excitations (aeroelastic flutter). In this talk, we consider an idealized fluid-structure interaction: a coupled heat-wave system, with a time-periodic external force. For undamped systems, the phenomenon of resonance can occur. For heat-type systems it cannot, and the existence and uniqueness theory of periodic solutions is well-established. Yet the case of coupled heat-wave systems is indeterminate, and periodicity is not characterized by the abstract theory of dissipative systems.
We will provide a construction of unique periodic solutions for this heat-wave system. A priori estimates will be achieved through boundary control methods, introducing geometric constraints into the problem. Thus, for certain classes of spatial domains, unique periodic solutions will be obtained from temporally smooth forcing, eliminating the possibility of resonance. We call attention to the "gap" between smoothness of the forcing and resulting solutions, and it remains open whether the geometric and regularity constraints are technical, or necessary to circumvent the emergence of resonance.