Lie symmetries and equivalence transformations for the Barenblatt-Gilman model

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:318

Article

Garrido, T. M.¹  Kasatkin, A. A.²  Bruzon, M. S.¹  Gazizov, R. K.² 

[1] Univ Cadiz, Dept Math, Cadiz, Spain

[2] Ufa State Aviat Tech Univ, Lab Grp Anal Math Models Nat & Engn Sci GAMMETT, Ufa, Russia

关键词: Barenblatt-Gilman equation;    Lie group analysis;    Equivalence transformations;    Travelling wave solutions;   

DOI  :  10.1016/j.cam.2016.09.023

来源: Elsevier

【 摘 要 】

In this paper we have considered the Barenblatt-Gilman equation which models the nonequilibrium countercurrent capillary impregnation. The equation of this model is a third-order equation and the unknown function concerns to the effective water saturation. We have applied the classical method to get the Lie group classification with respect to unknown function and we have constructed the equivalence transformations. We have also obtained the invariant solutions for some forms of the equation, including travelling wave solutions based on the Jacobi elliptic sine function. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free