Computer Assisted Proofs For A Nonlinear Laplace Beltrami Equation On The Sphere

Download or read book Computer-assisted Proofs for a Nonlinear Laplace-Beltrami Equation on the Sphere written by Gabriel Duchesne and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this study, we prove the existence and local uniqueness of radially symmetric solutions of nonlinear partial differential equations via a rigorous numerical method. We introduce the concepts of Banach spaces of geometrically decaying sequences and explore the domains of convergence of the Taylor and Chebyshev expansions. These notions constitute the basis for the Radii Polynomial Theorem on Banach spaces of infinite sequences, which is the main tool employed to obtain the proofs by using a combination of Taylor and Chebyshev coefficients of the solutions. We also introduce briefly the notions of interval analysis to justify the rigor of our computer-assisted results"--