Lifespan of solutions of a fractional evolution equation with higher order diffusion on the Heisenberg group
Date
2020-01-07
Authors
Alsaedi, Ahmed
Ahmad, Bashir
Kirane, Mokhtar
Nabti, Abderrazak
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the higher order diffusion Schrödinger equation with a time nonlocal nonlinearity
i∂tu - (-Δℍ)mu = λ/Γ(α) ∫t0 (t - s)α-1 |u(s)|pds,
posed in (η, t) ∈ ℍ x (0, +∞), supplemented with an initial data u(η, 0) = ƒ(η), where m > 1, p > 1, < α < 1, and Δℍ is the Laplacian operator on the (2N + 1)-dimensional Heisenberg group ℍ. Then, we prove a blow up result for its solutions. Furthermore, we give an upper bound estimate of the life span of blow up solutions.
Description
Keywords
Schrödinger equation, Heisenberg group, Life span, Riemann-Liouville fractional integrals and derivatives
Citation
Alsaedi, A., Ahmad, B., Kirane, M., & Nabti, A. (2020). Lifespan of solutions of a fractional evolution equation with higher order diffusion on the Heisenberg group. <i>Electronic Journal of Differential Equations, 2020</i>(02), pp. 1-10.
Rights
Attribution 4.0 International