Wellposedness, control, and observability theories for partial dierential equations
George Avalos (University of Nebraska-Lincoln), Scott Hansen (Iowa State
University), and Daniel Toundykov (University of Nebraska-Lincoln)
Our mini-symposium will concern analysis of partial differential equations (PDE's),
especially of those arising in engineering and physical sciences, with the focus on their
well-posedness and control-theoretic properties. There will be some emphasis on systems
whose characteristics are of "mixed type" such as
uid-structure interactions, possibly
with moving interfaces, structure-acoustic models, composite "sandwich" beams that
are described by multiple coupled elastic PDE's, etc.
The participants in our mini-symposium will be internationally recognized pioneers and
contributors in the mathematical control of infinite-dimensional systems. In addition to
the intrinsic merit of our proposed forum to have renowned experts present their work,
there is the possibility for further advancement in the field, by virtue of the opportunity
for discussion and future collaboration.
Particular examples of topics which would fall under the scope of our proposed sessions
include, though are not limited to:
(i) Methods of harmonic analysis, semigroup theory, monotone operator theory, and
functional-analytic techniques that help establish local well-posedness of solutions to
PDE's and their regularity.
(ii) Energy methods to infer a priori bounds for global existence or blow-up, compactness
ow and formation of attractors.
(iii) The optimal control of PDE's with respect to given quadratic or non-quadratic cost
(iv) Stabilization of given PDE dynamics by means of dissipation-enhancing feedback
control mechanisms localized either to the boundary of the physical domain wherein the
dynamics evolves, or to subsets of the interior of the said domain.
(iii) The exact steering or controlling of solutions of certain PDE dynamics through
the implementation of control functions, which are either supported on the boundary
or locally supported within the domain.