Group invariant solutions and local conservation laws of heat conduction equation arising laser heating carbon nanotubes using Lie group analysis

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Yaşar E. , Yıldırım Y.

Mathematical Sciences and Applications E-Notes, vol.10, no.2, pp.102-113, 2022 (Refereed Journals of Other Institutions)

  • Publication Type: Article / Article
  • Volume: 10 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.36753/mathenot.926867
  • Title of Journal : Mathematical Sciences and Applications E-Notes
  • Page Numbers: pp.102-113


In this study, based on the continuous transformations of Lie groups, the exact analytic solutions of the

laser heating carbon nanotubes formulated by using the classical heat conduction equation with various

physical properties were constructed. These solutions are the type of group invariant solutions. The

constructed solutions have expanded and enriched the solution forms of this new model existing in the

literature. With the help of the Maple package program, 3D, density, and contour graphs were drawn

for the special values of the parameters in the solutions, and the physical structures of the solutions

obtained in this way were also observed. The solutions obtained can be used in the explanation of

physical phenomena occurring in cancer investigations.