Guided Dynamical Systems and Applications to Functional and Partial Differential Equations
arXiv:math/0511638
Abstract
In this thesis we introduce the concept of a guided dynamical system, and exploit this idea to solve various problems in functional equations and PDE's. Our main results are 1) a necessary and sufficient condition for unique-solvability of an initial value functional equation, 2) a proof of the overdeterminedness of a large class of functional equations and 3) a necessary and sufficient condition for unique-solvability of a boundary value problem for a third order, hyperbolic PDE.
M.Sc. Thesis (Technion, IIT), 60 Pages, under the supervision of Prof. Boris Paneah; acknowledgements corrected