Computer-assisted proofs for radially symmetric solutions of PDEs

Autor:	János Dudás, Julien Courtois, István Balázs, Jan Bouwe van den Berg, Anett Vörös-Kiss, Jean-Philippe Lessard, J. F. Williams, Xi Yuan Yin
Přispěvatelé:	Mathematics
Rok vydání:	2018
Předmět:	Computational Mathematics Pure mathematics Nonlinear system symbols.namesake Partial differential equation Computational Mechanics Banach space Taylor series symbols Contraction mapping Mathematical proof Contraction (operator theory) Mathematics
Zdroj:	van den Berg, J B, Balázs, I, Courtois, J, Dudás, J, Vörös-Kiss, A, Yin, X Y, Williams, J F & Lessard, J-P 2018, ' Computer-assisted proofs for radially symmetric solutions of PDEs ', Journal of Computational Dynamics, vol. 5, no. 1&2, pp. 61-80 . https://doi.org/10.3934/jcd.2018003 Journal of Computational Dynamics, 5(1&2), 61-80. American Institute of Mathematical Sciences
ISSN:	2158-2505
Popis:	We obtain radially symmetric solutions of some nonlinear (geometric) 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2434625bbef322d458fb7ecd7f546417 https://doi.org/10.3934/jcd.2018003 Zobrazit plný text záznamu