An Algorithm for Constructing Lyapunov Functions
by Sigurdur Freyr Hafstein
Number of pages: 100
In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems, possessing a uniformly asymptotically stable equilibrium. We give numerous examples of Lyapunov functions constructed by our method at the end of the monograph.
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by R. E. Showalter - Pitman
Written for beginning graduate students of mathematics, engineering, and the physical sciences. It covers elements of Hilbert space, distributions and Sobolev spaces, boundary value problems, first order evolution equations, etc.
by Semyon Dyatlov, Maciej Zworski - MIT
Contents: Scattering resonances in dimension one; Resonances for potentials in odd dimensions; Black box scattering in Rn; The method of complex scaling; Perturbation theory for resonances; Resolvent estimates in semiclassical scattering; etc.
by Richard B. Melrose, Gunther Uhlmann - MIT
The origin of scattering theory is the study of quantum mechanical systems. The scattering theory for perturbations of the flat Laplacian is discussed with the approach via the solution of the Cauchy problem for the corresponding perturbed equation.
by Per Kristen Jakobsen - arXiv.org
These lecture notes view the subject through the lens of applied mathematics. The physical context for basic equations like the heat equation, the wave equation and the Laplace equation are introduced early on, and the focus is on methods.