F. Weissler

activity

20172020

collaborators

5 papers

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.AP2020

Sign-changing solutions of the nonlinear heat equation with persistent singularities

Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1

We study the existence of sign-changing solutions to the nonlinear heat equation $\partial_{t} u = Δ u + ∣ u ∣^{α} u$ on $R^{N}$ , $N \geq 3$ , with $\frac{2}{N - 2} < α < α_{0}$ , where…

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.AP2018

Perturbations of self-similar solutions

Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1

We consider the nonlinear heat equation $u_{t} = Δ u + ∣ u ∣^{α} u$ with $α > 0$ , either on $R^{N}$ , $N \geq 1$ , or on a bounded domain with Dirichlet boundary conditions. We prove th…

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…