62 citations · 261 across the 45 of their papers we have counts for
61 papers
Soliton Resolution at Blow-Up for the Subconformal Nonlinear Wave Equation
Hatem Zaag
We consider the nonlinear wave equation (NLW) with a superlinear pure power nonlinearity in the subconformal and conformal cases. Under some conditions on initial data, this equati…
On a Keller-Segel type equation to model Brain Microvascular Endothelial Cells growth's patterns
B Ambrosio, A Garroudji, S. Fitzsimons +2
This article presents a partial differential equation (PDE) of Keller-Segel (KS) type that reproduces patterns commonly observed during the growth of brain microvasculature. We pro…
Regularity and singularity of the blow-up curve for a wave equation with a derivative nonlinearity and a scale-invariant damping
Ahmed Bchatnia, Makram Hamouda, Firas Kaabi +2
In this article, we investigate the blow-up behavior of solutions to the one-dimensional damped nonlinear wave equation, namely $$ \partial_t^2 u - \partial_x^2 u + \fracμ{1 + t} \…
Feedback approximate controllability of blowup points for the heat equation with anti-interference blowup profile
Ping Lin, Hatem Zaag
This paper is concerned with a feedback approximate controllability problem of blowup points for the heat equation. We show that the system is approximately controllable for blowup…
Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation
Asma Azaiez, Jacek Jendrej, Hatem Zaag
This paper deals with blow-up for the complex-valued semilinear wave equation with power nonlinearity in dimension 1. Up to a rotation of the solution in the complex plane, we show…
Radial blow-up standing solutions for the semilinear wave equation
Maissâ Boughrara, Hatem Zaag
We consider the semilinear wave equation with a power nonlinearity in the radial case. Given , we construct a blow-up solution such that the solution near con…