62 citations · 261 across the 45 of their papers we have counts for
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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…
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…
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…
Standing Sphere Blow-up Solutions to The Nonlinear Heat Equation
Senhao Duan, Nejla Nouaili, Hatem Zaag
In this paper, we construct a singular standing ring solution of the nonlinear heat in the radial case. We give rigorous proof for the existence of a ring blow-up solution in finit…
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…