Differential Invariants for Two and Three Dimensional Linear Parabolic Equations

  • Adnan AslamEmail author
  • Asghar Qadir
  • Muhammad Safdar
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 266)


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.


Semi-invariants Joint differential invariants Lie infinitesimal method 


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Authors and Affiliations

  1. 1.Department of Basic Sciences, School of Electrical Engineering and Computer Science (SEECS)National University of Sciences and Technology (NUST)IslamabadPakistan
  2. 2.School of Natural Sciences (SNS)National University of Sciences and Technology (NUST)IslamabadPakistan
  3. 3.School of Mechanical and Manufacturing Engineering (SMME)National University of Sciences and Technology (NUST)IslamabadPakistan

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