Zobrazeno 1 - 10
of 267
pro vyhledávání: '"Zaag Hatem"'
Autor:
Boughrara, Maissâ, Zaag, Hatem
We consider the semilinear wave equation with a power nonlinearity in the radial case. Given $r_0>0$, we construct a blow-up solution such that the solution near $(r_0,T(r_0))$ converges exponentially to a soliton. Moreover, we show that $r_0$ is a n
Externí odkaz:
http://arxiv.org/abs/2410.00636
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 finite time. This result was predicted formally by Baruch, Fibich and Gavis
Externí odkaz:
http://arxiv.org/abs/2406.04422
Autor:
Hamza, Mohamed Ali, Zaag, Hatem
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 some space-time integral, showing a $|\log(T-t)|^q$ improvement in com
Externí odkaz:
http://arxiv.org/abs/2405.18611
We develop a hybrid scheme based on a finite difference scheme and a rescaling technique to approximate the solution of nonlinear wave equation. In order to numerically reproduce the blow-up phenomena, we propose a rule of scaling transformation, whi
Externí odkaz:
http://arxiv.org/abs/2309.05358
Autor:
Roy, Tristan, Zaag, Hatem
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 by the solution of the associated ODE which has the same blow-up time.
Externí odkaz:
http://arxiv.org/abs/2308.12220
In this paper, we consider the complex Ginzburg-Landau equation $$ \partial_t u = (1 + i \beta) \Delta u + (1 + i \delta) |u|^{p-1}u - \alpha u, \quad \text{where } \beta, \delta, \alpha \in \mathbb{R}. $$ The study focuses on investigating the finit
Externí odkaz:
http://arxiv.org/abs/2308.02297
Autor:
Rebai, Ahmed, Boukhris, Louay, Toujani, Radhi, Gueddiche, Ahmed, Banna, Fayad Ali, Souissi, Fares, Lasram, Ahmed, Rayana, Elyes Ben, Zaag, Hatem
We propose to explore the potential of physics-informed neural networks (PINNs) in solving a class of partial differential equations (PDEs) used to model the propagation of chronic inflammatory bowel diseases, such as Crohn's disease and ulcerative c
Externí odkaz:
http://arxiv.org/abs/2302.07405
Autor:
Huang, Yi C., Zaag, Hatem
In a recent work, Duong, Ghoul and Zaag determined the gradient profile for blowup solutions of standard semilinear heat equation with power nonlinearities in the (supposed to be) generic case. Their method refines the constructive techniques introdu
Externí odkaz:
http://arxiv.org/abs/2210.14773
In this paper, we revisit the proof of the existence of a solution to the semilinear heat equation in one space dimension with a at blowup profile, already proved by Bricmont and Kupainen together with Herrero and Vel\'{a}zquez. Though our approach r
Externí odkaz:
http://arxiv.org/abs/2206.04378
Autor:
Merle, Frank, Zaag, Hatem
We consider the semilinear heat equation with a superlinear power nonlinearity in the Sobolev subcritical range. We construct a solution which blows up in finite time only at the origin, with a completely new blow-up profile, which is cross-shaped. O
Externí odkaz:
http://arxiv.org/abs/2205.06795