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Volume 5, Issue 2, May 1998, Pages 115 - 119
On a Class of Linearizable Monge-Ampère Equations
Authors
D.J. Arrigo, J.M. Hill
Corresponding Author
D.J. Arrigo
Received 21 November 1997, Accepted 25 November 1997, Available Online 1 May 1998.
- DOI
- 10.2991/jnmp.1998.5.2.1How to use a DOI?
- 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
- © 2006, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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Cite this article
TY - JOUR AU - D.J. Arrigo AU - J.M. Hill PY - 1998 DA - 1998/05/01 TI - On a Class of Linearizable Monge-Ampère Equations JO - Journal of Nonlinear Mathematical Physics SP - 115 EP - 119 VL - 5 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.1998.5.2.1 DO - 10.2991/jnmp.1998.5.2.1 ID - Arrigo1998 ER -