Rigorous Numerical Verification of Uniqueness and Smoothness in a Surface Growth Model

  • Based on numerical data and a-posteriori analysis we verify rigorously the uniqueness and smoothness of global solutions to a scalar surface growth model with striking similarities to the 3D Navier–Stokes equations, for certain initial data for which analytical approaches fail. The key point is the derivation of a scalar ODE controlling the norm of the solution, whose coefficients depend on the numerical data. Instead of solving this ODE explicitly, we explore three different numerical methods that provide rigorous upper bounds for its solution.

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Author:Dirk BlömkerORCiDGND, Christian Nolde, James Robinson
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/2448
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2013-16)
Year of first Publication:2013
Publishing Institution:Universität Augsburg
Release Date:2013/08/29
Tag:suface growth; a-posteriori regularity
GND-Keyword:Nichtlineare Differentialgleichung; Wachstumsmodell; Regularität
Erschienen in Journal of Mathematical Analysis and Applications, 429, 1, S. 311-325, https://doi.org/10.1016/j.jmaa.2015.04.025
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand