10 papers
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}…
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…
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…
The blow-up rate for a loglog non-scaling invariant semilinear wave equation
Tristan Roy, Hatem Zaag
We consider blow-up solutions of a semilinear wave equation with a loglog perturbation of the power nonlinearity in the subconformal case, and show that the blow-up rate is given b…
A better bound on blow-up rate for the superconformal semilinear wave equation
Mohamed Ali Hamza, Hatem Zaag
We consider the semilinear wave equation in higher dimensions with superconformal power nonlinearity. The purpose of this paper is to give a new upper bound on the blow-up rate in…