Classical Symmetries for Two Special Cases of Unsteady Flow in Nanoporous Rock

  • Tamara M. GarridoEmail author
  • Rafael de la Rosa
  • María Santos Bruzón
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 18)


In the present paper, we study two equations related to the theory of fluid and gas flow in nanoporous media. Both models are special cases of the basic equation of the unsteady flow in nanoporous rock, the first one is the case of weakly compressible fluid and the second one of the case of isothermic gas flow. Moreover, a generalization of the equations is presented to study thoroughly the physical phenomena. This new generalized equations involve arbitrary functions. Lie method is applied to the model of generalized unsteady flow and the model of generalized isothermic gas flow. Finally a classification in different cases depending on the arbitrary function is shown.


Lie point symmetries Contact symmetries Weakly compressible fluid Isothermic gas flow Nanoporous rock 



The authors gratefully thank the Universidad Politécnica de Cartagena for their support. The authors are grateful to the Junta de Andalucía for the financial support of group FQM-201 and they express their sincere gratitude to the Plan Propio de Investigación de la Universidad de Cádiz. Authors warmly thank the referee for suggestions to improve the paper.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tamara M. Garrido
    • 1
    Email author
  • Rafael de la Rosa
    • 1
  • María Santos Bruzón
    • 1
  1. 1.Departamento de MatemáticasUniversidad de CádizCádizSpain

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