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title:
 
On a Class of Linearizable Monge-Ampère Equations
publication:
 
JNMP
volume-issue:   5 - 2
pages:   115 - 119
ISSN:
  1402-9251
DOI:
  doi:10.2991/jnmp.1998.5.2.1 (how to use a DOI)
author(s):
 
D.J. ARRIGO, J.M. HILL
publication date:
 
May 1998
abstract:
 
Monge-Ampère equations of the form, uxxuyy - u2 xy = F(u, ux, uy) arise in many areas of fluid and solid mechanics. Here it is shown that in the special case F = u4 yf(u, ux/uy), where f denotes an arbitrary function, the Monge-Ampère equation can be linearized by using a sequence of Ampère, point, Legendre and rotation transformations. This linearization is a generalization of three examples from finite elasticity, involving plane strain and plane stress deformations of the incompressible perfectly elastic Varga material and also relates to a previous linearization of this equation due to Khabirov [7].
copyright:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
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