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Computer-assisted proofs in PDE: a survey

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Abstract

In this survey we present some recent results concerning computer-assisted proofs in partial differential equations, focusing in those coming from problems in incompressible fluids. Particular emphasis is put on the techniques, as opposed to the results themselves.

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Acknowledgements

J.G.-S. was partially supported by the Grant MTM2014-59488-P (Spain), by the ICMAT-Severo Ochoa Grant SEV-2015-0554, by the Simons Collaboration Grant 524109 and by the NSF-DMS 1763356 Grant. We would like to thank Diego Córdoba, Jordi-Lluís Figueras and Francisco Gancedo for helpful comments on previous versions of this manuscript. This paper was developed out of a talk given at the XVIII Spanish-French School Jacques-Louis Lions about Numerical Simulation in Physics and Engineering, where I was awarded the 2018 Antonio Valle Prize from the Sociedad Española de Matemática Aplicada (SeMA). I would like to thank the SeMA and the organizers of the conference for such a great opportunity.

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Gómez-Serrano, J. Computer-assisted proofs in PDE: a survey. SeMA 76, 459–484 (2019). https://doi.org/10.1007/s40324-019-00186-x

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