Computer-assisted proofs for radially symmetric solutions of PDEs
2018
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.
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