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Differential invariants for a class of diffusion equations

We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional.The equivariant moving frame methodology is invoked to construct, in the regular case of the normalization procedure, a moving frame for a group related...

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Bibliographic Details
Date:2019
Author Affiliations:
  • E. Dos Santos Cardoso-Bihlo — Memorial University of Newfoundland
  • A. Bihlo — Memorial University of Newfoundland
  • R. Popovych — Institute of Mathematics of NAS of Ukraine; Universitat Wien
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Main Authors: Dos Santos Cardoso-Bihlo, E., Bihlo, A., Popovych, R., Дос Сантос Кардозо-Біло, E., Біло, А., Попович, Р.
Format: Article
Language:English
Published: Інститут математики НАН України 2019
Online Access:https://trim.imath.kiev.ua/index.php/trim/article/view/367
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Journal Title:Transactions of Institute of Mathematics of NAS of Ukraine
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Transactions of Institute of Mathematics of NAS of Ukraine
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Summary:We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional.The equivariant moving frame methodology is invoked to construct, in the regular case of the normalization procedure, a moving frame for a group related to the equivalence group in the context of equivalence transformations among equations of the class under consideration.Using the moving frame constructed, we describe the algebra of differential invariants of the former group by obtaining a minimum generating set of differential invariants and a complete set of independent operators of invariant differentiation.

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