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Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an ...
Sobolev Gradient Flows and Image Processing
In this thesis we study Sobolev gradient flows for Perona-Malik style energy functionals and generalizations thereof. We begin with first order isotropic flows which are shown to be regularizations of the heat equation. ...
Controllability of Underactuated Coupled Parabolic Systems
This thesis studies the null controllability of a system of coupled parabolic PDEs. Moreover, our work specializes to an important subclass of these control problems, where systems are underactuated and are coupled by first ...