S. Tayachi

activity

20132021

most citedGlobal existence and scattering for the inhomogeneous nonlinear Schrödinger equation

1 citations · 1 across the 6 of their papers we have counts for

collaborators

6 papers

math.AP2021★ 1 cited

Global existence and scattering for the inhomogeneous nonlinear Schrödinger equation

Lassaad Aloui, Slim Tayachi

In this paper we consider the inhomogeneous nonlinear Schrödinger equation $i \partial_{t} u + Δ u = K (x) ∣ u ∣^{α} u, u (0) = u_{0} \in H^{s} (R^{N}), s = 0, 1,$ $N \geq 1,$ $|K(x)|+|x|^s|\na…

math.AP2019

Large time behavior of solutions to the nonlinear heat equation with absorption with highly singular antisymmetric initial values

Hattab Mouajria, Slim Tayachi, Fred B. Weissler

In this paper we study global well-posedness and long time asymptotic behavior of solutions to the nonlinear heat equation with absorption, $u_{t} - Δ u + ∣ u ∣^{α} u = 0$ , where $u=u(t,x)…

math.AP2019

Global existence and decay estimates for the heat equation with exponential nonlinearity

Mohamed Majdoub, Slim Tayachi

In this paper we consider the initial value {problem $\partial_{t} u - Δ u = f (u),$ $u (0) = u_{0} \in e x p L^{p} (R^{N}),$ } where $p > 1$ and $f : R \to R$ having an expon…

math.AP2017

The nonlinear heat equation involving highly singular initial values and new blowup and life span results

Slim Tayachi, Fred B. Weissler

In this paper we prove local existence of solutions to the nonlinear heat equation $u_t = Δu +a |u|^αu, \; t\in(0,T),\; x=(x_1,\,\cdots,\, x_N)\in {\mathbb R}^N,\; a = \pm 1,\; α>0…

math.AP2015

Existence of a Stable Blow-up profile for the nonlinear heat equation with a critical power nonlinear gradient term

Slim Tayachi, Hatem Zaag

We consider the nonlinear heat equation with a nonlinear gradient term: $\partial_{t} u = Δ u + μ ∣\nabla u ∣^{q} + ∣ u ∣^{p - 1} u, μ > 0, q = 2 p / (p + 1), p > 3, t \in (0, T), x \in R^{N} .$ We const…

math.AP2013

Remarks on the Cauchy problem for the one-dimensional quadratic (fractional) heat equation

Luc Molinet, Slim Tayachi

We prove that the Cauchy problem associated with the one dimensional quadratic (fractional) heat equation: $u_{t} = D_{x}^{2 α} u \mp u^{2}, t \in (0, T), x \in R$ or $ \T $, with $ 0<α\l…