Computer-assisted proofs for radially symmetric solutions of PDEs

Balázs, István and Bouwe van den Berg, Jan and Courtois, Julien and Dudás, János and Lessard, Jean-Philippe and Vörös-Kiss, Anett and Williams, JF and Yin, Xi Yuan (2018) Computer-assisted proofs for radially symmetric solutions of PDEs. Journal of Computational Dynamics, 5 (1-2). pp. 61-80.

Preview	Text compuproofsDEs.pdf - Submitted Version Download (964kB) | Preview
	Text computer_assisted_proofs_for_radially_symmetric_solutions_of_pdes.pdf - Published Version Restricted to Repository staff only Download (1MB)

Abstract

We obtain radially symmetric solutions of some nonlinear (geo- metric) partial differential equations via a rigorous computer-assisted method. We introduce all main ideas through examples, accessible to non-experts. The proofs are obtained by solving for the coefficients of the Taylor series of the solutions in a Banach space of geometrically decaying sequences. The tool that allows us to advance from numerical simulations to mathematical proofs is the Banach contraction theorem.

Actions (login required)

Edit Item