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math.AP2022
On inhomogeneous heat equation with inverse square potential
Divyang G. Bhimani, Saikatul Haque
We study inhomogeneous heat equation with inverse square potential, namely, \[\partial_tu + \mathcal{L}_a u= \pm |\cdot|^{-b} |u|^αu,\] where We est…
math.AP2022★ 1 cited
On heat equations associated with fractional harmonic oscillators
Divyang G. Bhimani, Ramesh Manna, Fabio Nicola +2
We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator , , associated with the harmonic oscillator . We…
math.AP2022★ 1 cited
Normalized solutions to nonlinear Schrödinger equations with competing Hartree-type nonlinearities
Divyang Bhimani, Tianxiang Gou, Hichem Hajaiej
In this paper, we consider solutions to the following nonlinear Schrödinger equation with competing Hartree-type nonlinearities, $$ -Δu + λu=\left(|x|^{-γ_1} \ast |u|^2\right) u -…