S. Tayachi

activity

20132026

most citedLocal well-posedness and global existence for the biharmonic heat equation with exponential nonlinearity

6 citations · 12 across the 15 of their papers we have counts for

collaborators

17 papers

math.AP2026

Threshold for the existence of scattering states for inhomogeneous nonlinear Schrödinger equations without gauge invariance

Mourad Grira, Hayato Miyazaki, Slim Tayachi

We consider the asymptotic behavior of solutions to inhomogeneous nonlinear Schrödinger equations with non-gauge-invariant nonlinearities. The spatial coefficient in the nonlinear…

math.AP2025

Asymptotically self-similar global solutions for Hardy-Hénon parabolic equations

Noboru Chikami, Masahiro Ikeda, Koichi Taniguchi +1

We construct asymptotically self-similar global solutions to the Hardy-Hénon parabolic equation $\partial_{t} u - Δ u = \pm ∣ x ∣^{γ} ∣ u ∣^{α - 1} u$ , $α > 1$ , $γ \in R$ for a large cl…

math.AP2023

Asymptotic behavior and life-span estimates for the damped inhomogeneous nonlinear Schrödinger equation

Lassaad Aloui, Sirine Jbari, Slim Tayachi

We are interested in the behavior of solutions to the damped inhomogeneous nonlinear Schrödinger equation $i \partial_{t} u + Δ u + μ ∣ x ∣^{- b} ∣ u ∣^{α} u + ia u = 0$ , $μ \in C$ , $b > 0$ , $a \in…

math.AP2023

Unconditional uniqueness and non-uniqueness for Hardy-Hénon parabolic equations

Noboru Chikami, Masahiro Ikeda, Koichi Taniguchi +1

We study the problems of uniqueness for Hardy-Hénon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (H…

math.AP2022

New life-span results for the nonlinear heat equation

Slim Tayachi, Fred B. Weissler

We obtain new estimates for the existence time of the maximal solutions to the nonlinear heat equation $\partial_{t} u - Δ u = ∣ u ∣^{α} u, α > 0$ with initial values in Lebesgue, weighted Lebes…

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.AP2020★ 4 cited

Relaxation to equilibrium in the one-dimensional thin-film equation with partial wetting

Mohamed Majdoub, Nader Masmoudi, Slim Tayachi

We investigate the large time behavior of compactly supported solutions for a one-dimensional thin-film equation with linear mobility in the regime of partial wetting. We show the…

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.AP2016★ 1 cited

Existence and stability of a blow-up solution with a new prescribed behavior for a heat equation with a critical nonlinear gradient term

Slim Tayachi, Hatem Zaag

We consider the semilinear heat equation, to which we add a nonlinear gradient term, with a critical power. We construct a solution which blows up in finite time. We also give a sh…

math.AP2016★ 6 cited

Local well-posedness and global existence for the biharmonic heat equation with exponential nonlinearity

Mohamed Majdoub, Sarah Otsmane, Slim Tayachi

In this paper we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $\partial_{t} u + Δ^{2} u = f (u), t > 0, x \in R^{N},$ with $f(u)\sim \mbox{e}^{u^2}$ for larg…

math.AP2016

Existence and regularity of source-type self-similar solutions for stable thin-film equations

Mohamed Majdoub, Slim Tayachi

We investigate the existence and the boundary regularity of source-type self-similar solutions to the thin-film equation $h_{t} = - (h^{n} h_{z z z})_{z} + (h^{n + 3})_{z z},$ $ t>0,\; z\in \mathbb…

math.AP2015

Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities

Philippe Souplet, Slim Tayachi

We study positive blowing-up solutions of systems of the form: $u_{t} = δ_{1} Δ u + e^{p v}, v_{t} = δ_{2} Δ v + e^{q u},$ with $δ_{1}, δ_{2} > 0$ and $p, q > 0$ . We prove single-point blow-up for large…

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.AP2015

Improved conditions for single-point blow-up in reaction-diffusion systems

Nejib Mahmoudi, Philippe Souplet, Slim Tayachi

We study positive blowing-up solutions of the system: $u_{t} - δ Δ u = v^{p}, v_{t} - Δ v = u^{q},$ as well as of some more general systems. For any $p, q > 1$ , we prove single-point blo…

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…