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Wellposedness, control, and observability theories for partial dierential equations

Organizers:
George Avalos (University of Nebraska-Lincoln), Scott Hansen (Iowa State University), and Daniel Toundykov (University of Nebraska-Lincoln)

Abstract:
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 of the ow and formation of attractors.
(iii) The optimal control of PDE's with respect to given quadratic or non-quadratic cost functionals.
(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.