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A stability result of a fractional heat equation and time fractional diffusion equations governed by fractional fluxes in the Heisenberg group

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Abstract

Our research is divided into two parts. The first part studies the asymptotic behavior of a class of nonlocal diffusion problems in the fractional Sobolev–Slobodeckiĭ-spaces in the Heisenberg group by employing the theory of monotone operators and pullback attractors. In the second part of the manuscript, under some appropriate conditions, we study the well-posedness of a fractional time problem using fractional flows. To the best of our knowledge, this is the first time that fractional diffusion problems have been studied in the Heisenberg group.

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Acknowledgements

E. J. Hurtado has received a research grant Capes 001.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Brasília, Brasília, DF, 70297-400, Brazil

    E. J. Hurtado

  2. Facultad de Matemática, Universidade de Nacional Mayor San Marcos, Ciudad Universitaria - UNMSM, Av. República de Venezuela 3400, Lima, Peru

    A. P. Salvatierra

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  1. E. J. Hurtado
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Hurtado, E.J., Salvatierra, A.P. A stability result of a fractional heat equation and time fractional diffusion equations governed by fractional fluxes in the Heisenberg group. Rend. Circ. Mat. Palermo, II. Ser 72, 3869–3889 (2023). https://doi.org/10.1007/s12215-023-00866-8

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  • DOI: https://doi.org/10.1007/s12215-023-00866-8

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