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 |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-24480 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/2448 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2013-16) |
| Type: | Preprint |
| Language: | English |
| 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 |
| Note: | 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 |
