The University of Arizona

Scalings and saturation in infinite-dimensional control problems with applications to stochastic partial differential equations

Scalings and saturation in infinite-dimensional control problems with applications to stochastic partial differential equations

Series: Mathematical Physics and Probability Seminar
Location: Math 402
Presenter: David Herzog, Iowa State University

We discuss scaling methods which can be used to solve low mode control problems for nonlinear partial differential equations.  These methods lead naturally to a infinite-dimensional generalization of the notion of saturation, originally due to Jurdjevic and Kupka in the finite-dimensional setting of ODEs.  The methods will be highlighted by applying them to specific equations, including reaction-diffusion equations, the 2d/3d Euler/Navier-Stokes equations and the 2d Boussinesq equations.  Applications to support properties of the laws solving randomly-forced versions of each of these equations will be noted.

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