9 papers
Well-Posedness of a Coupled Brinkman--Biofilm--Nutrient System with Volume-Fraction Constraints
Azhar Alhammali, Mohamed Majdoub
We investigate a coupled system of partial differential equations modeling the interaction between Brinkman flow, biofilm evolution, and nutrient transport in a porous medium. The…
Fujita-type blow-up for inhomogeneous semilinear heat equations with regularly varying forcing
Vishvesh Kumar, Mohamed Majdoub
We develop a unified framework for Fujita-type blow-up of solutions to the inhomogeneous semilinear heat equation $$\partial_tu-Îu=|u|^p+\mathbf{w}(x), \qquad (t,x)\in(0,\infty)\t…
Fujita Phenomenon for a Mixed Local-Nonlocal Hardy-Hénon Equation with Regularly Varying Time Weights
Rihab Ben Belgacem, Mohamed Majdoub
We investigate the Cauchy problem for a semilinear parabolic equation driven by a mixed local-nonlocal diffusion operator of the form \[ \partial_t u - (Î- (-Î)^{\mathsf{s}})u =…
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…
On the Fujita Phenomenon for a Forced Spatio-Temporal Fractional Diffusion Equation
Rihab Ben Belgacem, Mohamed Majdoub
We investigate the Cauchy problem for a semilinear spatio--temporal fractional diffusion equation with a time-dependent forcing term: \[ \partial_t^αu + (-Î)^{\mathsf{s}} u = |u|…
The inhomogeneous fractional stochastic heat equation driven by fractional Brownian motion
R. Alessa, R. Al Subaie, M. Alwohaibi +2
We investigate the fractional Hardy-Hénon equation with fractional Brownian noise where $…