4 citations · 6 across the 21 of their papers we have counts for
22 papers
Normalized ground states and a mass-constrained scattering threshold for the inhomogeneous NLS with an inverse-square potential
Mohamed Majdoub, Tarek Saanouni
We study the focusing inhomogeneous nonlinear Schrödinger equation with an inverse-square potential $$ i\partial_t u+Δu-a|x|^{-2}u+|x|^{-b}|u|^αu=0, \qquad (t,x)\in\mathbb{R}\times…
Remarks on the well-posedness of the energy-critical inhomogeneous Hartree equation
Seongyeon Kim, Tarek Saanouni, Ihyeok Seo
We study the energy-critical inhomogeneous Hartree equation in space dimensions three and higher. Previous local well-posedness results left open the parameter regime where the inh…
Normalized Standing Waves for the Focusing Inhomogeneous Schrödinger Equation with Spatially Growing Nonlinearity
Mohamed Majdoub, Tarek Saanouni
We study the focusing inhomogeneous nonlinear Schrödinger equation with and .…
Biharmonic non-linear Schrödinger equation with an unbounded inhomogeneous term
Taif Abdullah Enaoufal, Tarek Saanouni
This paper is devoted to the analysis of a focusing nonlinear biharmonic Schrödinger equation in the presence of an unbounded growing up inhomogeneous term. The first main contribu…
A note on the fourth-order Schrodinger equation with spatially growing inhomogeneous source term
Alaa Mohammed Alqaied, Tarek Saanouni
This paper studies a non-linear biharmonic Schödinger equation with an unbounded inhomogeneous term. The main goal is to develop a local theory but also a global theory for small d…
Damping Effects on Global Existence and Scattering for an Inhomogeneous NLS Equation with Inverse-Square Potential
Makram Hamouda, Mohamed Majdoub, Tarek Saanouni
This work explores the global existence and scattering behavior of solutions to a damped, inhomogeneous nonlinear Schrodinger equation featuring a time-dependent damping term, an i…
Sharp threshold of scattering versus non-scattering for some mass-sub-critical inhomogeneous NLS
B. Ayed. Sabria, T. Saanouni
This work investigates the long time asymptotic behavior of some inhomogeneous non-linear Schrödinger type equations. We give sharp a threshold of scattering versus non-scattering…
Radial 3D Focusing Energy Critical INLS equations with defocusing perturbation: Ground states, Scattering, and Blow-up
Tianxiang Gou, Mohamed Majdoub, Tarek Saanouni
We investigate the following inhomogeneous nonlinear Schrödinger equation in the radial regime, featuring a focusing energy-critical nonlinearity and a defocusing perturbation: $$…
Non-radial Blow-up for a mass-critical fourth-order inhomogeneous nonlinear Schrödinger equation
Ruobing Bai, Mohamed Majdoub, Tarek Saanouni
We investigate the blow-up for a fourth-order Schrödinger equation with a mas-critical focusing inhomogeneous nonlinearity. We prove the finite/infinite-time blow-up of non-radial…
NLS equation with competing inhomogeneous nonlinearities: ground states, blow-up, and scattering
Tianxiang Gou, Mohamed Majdoub, Tarek Saanouni
We investigate a class of nonlinear equations of Schrödinger type with competing inhomogeneous nonlinearities in the non-radial inter-critical regime, \begin{align*} i \partial_t u…
Finite time blow-up of non-radial solutions for some inhomogeneous Schrödinger equations
Ruobing Bai, Tarek Saanouni
This work studies the inhomogeneous Schrödinger equation Here, $s\in\{1,2…
Energy-critical inhomogeneous generalized Hartree equation with inverse square potential
Seongyeon Kim, Tarek Saanouni
This work studies the Cauchy problem for the energy-critical inhomogeneous Hartree equation with inverse square potential $$i\partial_t u-\mathcal K_λu=\pm |x|^{-τ}|u|^{p-2}(I_α*|\…
Well-posedness and scattering for a 2D inhomogeneous NLS with Aharonov-Bohm magnetic potential
Mohamed Majdoub, Tarek Saanouni
We consider the magnetic nonlinear inhomogeneous Schrödinger equation $$i\partial_t u -\left(-i\nabla+\fracα{|x|^2}(-x_2,x_1)\right)^2 u =\pm|x|^{-\varrho}|u|^{p-1}u,\quad (t,x)\in…
Long time dynamics for the focusing inhomogeneous fractional Schrödinger equation
Mohamed Majdoub, Tarek Saanouni
We consider the following fractional NLS with focusing inhomogeneous power-type nonlinearity $$i\partial_t u -(-Δ)^s u + |x|^{-b}|u|^{p-1}u=0,\quad (t,x)\in \mathbb{R}\times \mathb…
Scattering for a class of non-radial inhomogeneous bi-harmonic Hartree equations
Tarek Saanouni, Hanene Hezzi
This manuscript proves the energy scattering of global solutions to a repulsive fourth-order generalized Hartree equation with non-radial data in the inter-critical regime. This wo…
Long time dynamics and blow-up for the focusing inhomogeneous nonlinear Schrödinger equation with spatial growing nonlinearity
Van Duong Dinh, Mohamed Majdoub, Tarek Saanouni
We investigate the Cauchy problem for the focusing inhomogeneous nonlinear Schrödinger equation in the radial Sobolev space $H^1_{\text{…
Energy scattering for radial focusing inhomogeneous bi-harmonic Schrödinger equations
Tarek Saanouni
This note studies the asymptotic behavior of global solutions to the fourth-order Schrödinger equation Indeed, for both cases, local and non-local sour…
Scattering for radial bi-harmonic Hartree equations
Tarek Saanouni
This note studies the asymptotic behavior of global solutions to the fourth-order generalized Hartree equation Indeed, for both attract…
Scattering theory for a class of radial focusing inhomogeneous Hartree equations
Tarek Saanouni
This paper studies the asymptotic behavior of global solutions to the generalized Hartree equation Indeed, using a new approa…
Remarks on the fractional inhomogeneous Hartree equation
Tarek Saanouni
This paper studies the inhomogeneous fractional Schödinger equation In the mass super-critical and energy sub-critical…
Double logarithmic inequality with a sharp constant in four space dimensions
Mohamed Majdoub, Tarek Saanouni
We prove a Log Log inequality with a sharp constant in four dimensions for radially symmetric functions. We also show that the constant in the Log estimate is almost sharp.
Well posedness and unconditional non uniqueness for a 2D semilinear heat equation
Slim Ibrahim, Rym Jrad, Mohamed Majdoub +1
We investigate the initial value problem for a semilinear heat equation with exponential-growth nonlinearity in two space dimension. First, we prove the local existence and uncondi…