Dhouha Draouil

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math.AP2024

Well-posedness and linearization for a semilinear wave equation with spatially growing nonlinearity

Dhouha Draouil, Mohamed Majdoub

We study the initial value problem for a defocusing semi-linear wave equation with spatially growing nonlinearity. By employing Moser-Trudinger type inequalities and Strichartz est…

math.AP2018

A 2D Schrodinger equation with time-oscillating exponential nonlinearity

Abdelwahab Bensouilah, Dhouha Draouil, Mohamed Majdoub

This paper deals with the 2-D Schrödinger equation with time-oscillating exponential nonlinearity $i \partial_{t} u + Δ u = θ (ω t) (e^{4 π ∣ u ∣^{2}} - 1)$ , where $θ$ is a periodic $C^{1}$ -fu…

math.AP2017

Energy critical Schrödinger equation with weighted exponential nonlinearity I: Local and global well-posedness

Abdelwahab Bensouilah, Dhouha Draouil, Mohamed Majdoub

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with weighted exponential nonlinearity $$ i\partial_t u+Δu=\frac{u}{|x|^b}(e^{α|u|^2}-1); \…