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Numerical Methods for Nonlinear Elliptic Differential EquationsA Synopsis$
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Klaus Boehmer

Print publication date: 2010

Print ISBN-13: 9780199577040

Published to Oxford Scholarship Online: January 2011

DOI: 10.1093/acprof:oso/9780199577040.001.0001

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From linear to nonlinear equations, fundamental results

From linear to nonlinear equations, fundamental results

Chapter:
(p.3) 1 From linear to nonlinear equations, fundamental results
Source:
Numerical Methods for Nonlinear Elliptic Differential Equations
Author(s):

Klaus Böhmer

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199577040.003.0001

Chapter 1 demonstrates, for the simple mechanical example of a bent rod, the change in character from linear to nonlinear regimes. This is followed by several examples for different types of nonlinear elliptic differential equations in mathematics, science and in engineering, e.g. the Monge‐Ampère, the reaction‐diffusion, the von Kármán and the Navièr‐Stokes equations. These problems require appropriate analytical results for (space‐) discretization methods. The necessary tools from functional analysis and calculus in Banach spaces are summarized.

Keywords:   linear regimes, nonlinear regimes, Monge‐Ampère, reaction‐diffusion, von Kármán equations, Navièr-Stokes equations, basic functional analysis, Banach spaces

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