Special Session 97: Analysis and Control of Nonlinear Partial Differential Equation Evolution Systems

It is intended that this Special Session will provide a platform from which renowned specialists in Partial Differential Equations (PDE) and/or Mathematical Control Theory will present their latest research on nonlinear and evolutionary PDE. We anticipate that our speakers will have expertise in a wide-ranging array of topics, possibly including: (i) qualitative and quantitative properties enjoyed by solutions to nonlinear partial differential equations of hyperbolic, parabolic, or of mixed type. Such properties might include global existence and uniqueness; availability of so-called “hidden”, or extra boundary trace regularity; for local wellposedness of solutions, with associated finite time blow-up. In addition, the topic of longtime behavior of solutions for given dissipative PDE could conceivably be broached by one or other of our Speakers, including the existence of attracting sets of finite dimension. (ii) Shape and sensitivity analysis of PDE, particularly with a view toward treating moving boundary phenomena. (iii) Optimization and control problems for nonlinear PDE processes, including the longstanding issue of globally controlling nonlinear hyperbolic PDE. Feedback control schemes to stabilize nonlinear and unstable PDE might also be under discussion in our Special Session, particularly if such schemes are amenable to numerical implementation. The Organizers of this Special Session are hopeful that this bringing together of the various Participants, from various parts of the globe, and each with his or her unique expertise, will spark fruitful discussions and possible future research work in nonlinear PDE control analysis.