6 papers
The Fujita exponent across an interface
Mohamed Majdoub, Ezzedine Mliki
We consider the semilinear parabolic equation \[ \partial_t u = Îu + 2\mathfrak{q}\,δ_{\mathbb{S}}\,\nabla u + |u|^{p-1}u \qquad \text{in } (0,\infty)\times\mathbb{R}^N, \] where…
Sharp Lifespan Estimates and Fujita Phenomena for Fractional Hardy-Hénon Type Parabolic Equations
Mohamed Majdoub, Berikbol T. Torebek
We study the lifespan of mild solutions to the fractional semilinear parabolic Cauchy problem with a Hardy--Hénon-type weight \[ u_t + (-Î)^s u = |x|^{-γ}\,|u|^p, \qquad (t,x)\i…
An extension of a critical Hardy--Rellich inequality: explicit constants and the sharp weight range
Mohamed Majdoub
We revisit the critical Hardy--Rellich inequalities recently established by Castro in "A critical Hardy--Rellich inequality (preprint, arXiv:2511.16537, 2025)". Using the classical…
Forcing Effects on Finite-Time Blow-Up in Degenerate and Singular Parabolic Equations
Mohamed Majdoub, Berikbol T. Torebek
We study the degenerate and singular parabolic equation with a forcing term \[ |x|^{Ï_1}u_t = Îu + |x|^{Ï_2}|u|^p + t^\varrho \mathbf{w}(x), \quad (t,x)\in(0,\infty)\times\mathb…
Mild Solutions for Time--Fractional Stochastic Nonlocal Diffusion Equations
M. Alwohaibi, D. Alsaleh, M. El-Beltagy +2
We study a time--space nonlocal diffusion equation driven by additive time--space white noise, where the time derivative is the Caputo derivative of order . The model c…
Long-Time Asymptotics for Subordinated Fractional Diffusion Equations
Mohamed Majdoub, Ezzedine Mliki
We study the long-time behavior of solutions to a class of evolution equations arising from random-time changes driven by subordinators. Our focus is on fractional diffusion equati…