Guided Dynamical Systems and Applications to Functional and Partial Differential Equations

Details Guided Dynamical Systems and Applications to Functional and Partial Differential Equations Guided Dynamical Systems and Applications to Functional and Partial Differential Equations

2005-11-26

arxiv.org/abs/math/0511638v2

Mathematics

Dynamical Systems

M.Sc. Thesis (Technion, IIT), 60 Pages, under the supervision of Prof. Boris Paneah; acknowledgements corrected

Scientific paper

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.

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