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pop@ams.org |
Control Methods in PDE-Dynamical Systems Sunday, July 3 – Thursday, July 7 Organizing Committee This conference is intended for two distinct research communities in partial differential equations (PDE): (1) the PDE-control community, which is focused on the study of control-theoretic properties of PDEs (e.g., well-posedness, interior and boundary regularity, controllability, stabilization, and optimization); and (2) the PDE-dynamical systems community, which is focused on the long-time behavior of solutions (e.g., global attractors and their geometric, topological, and structural properties). These communities, while pursuing different interests and using different methodologies, share a substantial body of common knowledge and background on evolutionary equations. The time is ripe and the momentum is propitious to bring them together at a joint conference. The main goal of this conference is to develop mutual stimulation and joint interactions, thereby leading to a marked advancement of the broader area of research. For example, recent research developments in these two communities suggest that this goal will be met, for the benefit of all. As an illustration, one may cite one of the goals of PDE-control research in this area: to force otherwise unstable dynamics to acquire good stability properties locally or, when possible, globally, by the insertion of a suitable feedback dissipative controller, possibly on the boundary. Thus the exchange of information and experience between these two mathematical groups is uniquely well-suited at this stage to produce significant advances on a broad spectrum of problems of control-theoretic and long-time behavior relevance. Dynamics to be considered encompass the following systems: (i) parabolic equations including equations of fluid dynamics with turbulent flows (such as Navier-Stokes equations); (ii) hyperbolic or Petrowski-like equations, including hyperbolic conservations laws and systems of nonlinear elasticity; (iii) systems of strongly coupled PDEs, whether they display a hyperbolic/hyperbolic coupling (such as in shell theory) or else a hyperbolic/parabolic coupling (such as in thermoelasticity and in structural acoustic chamber models). The timeliness of the conference is reinforced by the very recent breakthrough on the well-posedness theory of conservation laws, which opens the door to the treatment of related control problems. The organizers have secured a preliminary list of top specialists in both controlled PDE-systems and PDE-based dynamical systems. |
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