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

Hurtado E.J.; Salvatierra A.P. · Rendiconti del Circolo Matematico di Palermo (2023) · DOI: 10.1007/s12215-023-00866-8

Resumen

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.

Instituciones: Universidad Nacional Mayor de San Marcos