Lie symmetries and equivalence transformations for the Barenblatt-Gilman model

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• 作者：T.M. Garrido^a ; ^{tamara.garrido@uca.es} ; A.A. Kasatkin^b ; ^{alexei_kasatkin@mail.ru} ; M.S. Bruzó ; n^a ; ^{m.bruzon@uca.es} ; R.K. Gazizov^b ; ^{gazizov@mail.rb.ru}
• 关键词：Barenblatt&ndash ; Gilman equation ; Lie group analysis ; Equivalence transformations ; Travelling wave solutions
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：253-258
• 全文大小：385 K
• 卷排序：318

文摘

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.