[ Sur l'ellipticité des équations non linéaires pour une certaine classe de matériau isotrope et compressible ]
Volume 13, Issue 2, October 2015, Pages 327–334
Edouard Diouf1
1 Laboratoire de Mathématiques et Applications, Université de Ziguinchor, BP 523 Ziguinchor, Sénégal
Original language: French
Copyright © 2015 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Problems related to the elasticity, studied based on the models represented by the elliptic equations are characterized by their invariable in time. For an isotropic compressible medium, the loss of ellipticity criterion depends on the determinant of the Hessian matrix of the energy potential and therefore invariant tensor Cauchy Green. Necessary and sufficient conditions on the ellipticity or Legendre -Hadamard condition are given from two energy functions of polynomial type from the isotropic compressible case.
Author Keywords: nonlinear equation, compressibility, ellipticity, Legendre-Hadamard condition.
Volume 13, Issue 2, October 2015, Pages 327–334
Edouard Diouf1
1 Laboratoire de Mathématiques et Applications, Université de Ziguinchor, BP 523 Ziguinchor, Sénégal
Original language: French
Copyright © 2015 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Problems related to the elasticity, studied based on the models represented by the elliptic equations are characterized by their invariable in time. For an isotropic compressible medium, the loss of ellipticity criterion depends on the determinant of the Hessian matrix of the energy potential and therefore invariant tensor Cauchy Green. Necessary and sufficient conditions on the ellipticity or Legendre -Hadamard condition are given from two energy functions of polynomial type from the isotropic compressible case.
Author Keywords: nonlinear equation, compressibility, ellipticity, Legendre-Hadamard condition.
Abstract: (french)
Les problèmes liés à l'élasticité, étudiés sur la base des modèles représentés par les équations de type elliptique, se caractérisent par leur invariabilité dans le temps. Pour un milieu isotrope et compressible, le critère de perte d'ellipticité dépend du déterminant de la matrice hessienne du potentiel d'énergie et donc des invariants du tenseur de Cauchy Green. Des conditions nécessaires et suffisantes sur l'ellipticité ou condition de Legendre-Hadamard sont données à partir de deux fonctions d'énergie de type polynomial dans le cas isotrope et compressible.
Author Keywords: équations non linéaires, compressibilité, matrice hessienne, invariants, ellipticité.
How to Cite this Article
Edouard Diouf, “On the ellipticity of nonlinear equations for a certain class of isotropic material and compressible,” International Journal of Innovation and Applied Studies, vol. 13, no. 2, pp. 327–334, October 2015.
