TY - JOUR
T1 - Computer-assisted proofs for radially symmetric solutions of PDEs
AU - van den Berg, Jan Bouwe
AU - Balázs, István
AU - Courtois, Julien
AU - Dudás, János
AU - Vörös-Kiss, Anett
AU - Yin, Xi Yuan
AU - Williams, J.F.
AU - Lessard, Jean-Philippe
PY - 2018/12
Y1 - 2018/12
N2 - 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.
AB - 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.
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UR - https://www.aimsciences.org/article/doi/10.3934/jcd.2018003
U2 - 10.3934/jcd.2018003
DO - 10.3934/jcd.2018003
M3 - Article
SN - 2158-2505
VL - 5
SP - 61
EP - 80
JO - Journal of Computational Dynamics
JF - Journal of Computational Dynamics
IS - 1&2
ER -