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Differential Invariants for Two and Three Dimensional Linear Parabolic Equations

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Symmetries, Differential Equations and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 266))

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Abstract

We find equivalence transformations for linear parabolic equations having two and three spatial dimensions. Invariants associated with these higher dimensional linear parabolic equations are derived using the obtained set of equivalence transformations. We apply Lie infinitesimal method to deduce the associated invariants. We find first order invariants for the the higher dimensional parabolic equations due to an invertible change of the dependent and independent variables separately. Further, obtained invariants are employed to reduce these linear higher dimensional parabolic equations to their simplest forms.

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Author information

Authors and Affiliations

  1. Department of Basic Sciences, School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Islamabad, H-12, Pakistan

    Adnan Aslam

  2. School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, H-12, Pakistan

    Asghar Qadir

  3. School of Mechanical and Manufacturing Engineering (SMME), National University of Sciences and Technology (NUST), Islamabad, H-12, Pakistan

    Muhammad Safdar

Authors
  1. Adnan Aslam
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  2. Asghar Qadir
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  3. Muhammad Safdar
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Corresponding author

Correspondence to Adnan Aslam .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA, USA

    Victor G. Kac

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, USA

    Peter J. Olver

  3. Department of Mathematics and Statistics, Université de Montréal, Montréal, QC, Canada

    Pavel Winternitz

  4. Civil Engineering Dept, Div.of Mechanics, Istanbul Technical University, Civil Engineering Department, Div.of Mechanics, Maslak (Istanbul), Turkey

    Teoman Özer

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Aslam, A., Qadir, A., Safdar, M. (2018). Differential Invariants for Two and Three Dimensional Linear Parabolic Equations. In: Kac, V., Olver, P., Winternitz, P., Özer, T. (eds) Symmetries, Differential Equations and Applications. Springer Proceedings in Mathematics & Statistics, vol 266. Springer, Cham. https://doi.org/10.1007/978-3-030-01376-9_9

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