F. Weissler

activity

20122024

most citedFinite-time blowup for a complex Ginzburg-Landau equation

36 citations · 85 across the 12 of their papers we have counts for

collaborators

12 papers

math.AP2024

Self-similar solutions for the generalized fractional Korteweg-de Vries equation

Luc Molinet, Stéphane Vento, Fred Weissler

We consider the Cauchy problem for the generalized fractional Korteweg-de Vries equation $u_{t} + D^{α} u_{x} + u^{p} u_{x} = 0, 1 < α \leq 2, p \in N ∖ {0},$ with 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.AP2020★ 5 cited

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★ 6 cited

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…

math.AP2017★ 11 cited

Sign-changing self-similar solutions of the nonlinear heat equation with positive initial value

Thierry Cazenave, Flávio Dickstein, Ivan Naumkin +1

We consider the nonlinear heat equation $u_{t} - Δ u = ∣ u ∣^{α} u$ on $R^{N}$ , where $α > 0$ and $N \geq 1$ . We prove that in the range $0 < α < \frac{4}{N - 2}$ , for every $μ > 0$ , there…

math.AP2015★ 10 cited

A Fujita-type blowup result and low energy scattering for a nonlinear Schrö\-din\-ger equation

Thierry Cazenave, Simão Correia, Flávio Dickstein +1

In this paper we consider the nonlinear Schrö\-din\-ger equation $i u_{t} + Δ u + κ ∣ u ∣^{α} u = 0$ . We prove that if $α < \frac{2}{N}$ and $ℑ κ < 0$ , then every nontrivial $H^{1}$ -solution blow…

math.AP2015★ 4 cited

Non-regularity in Hölder and Sobolev spaces of solutions to the semilinear heat and Schrödinger equations

Thierry Cazenave, Flávio Dickstein, Fred B. Weissler

In this paper we study the Cauchy problem for the semilinear heat and Schrödinger equations, with the nonlinear term $f (u) = λ ∣ u ∣^{α} u$ . We show that low regularity of $f$ (i.e.,…

math.AP2013★ 13 cited

Standing waves of the complex Ginzburg-Landau equation

Thierry Cazenave, Flávio Dickstein, Fred B. Weissler

We prove the existence of nontrivial standing wave solutions of the complex Ginzburg-Landau equation $ϕ_{t} = e^{i θ} Δ ϕ + e^{iγ} ∣ ϕ ∣^{α} ϕ$ with periodic boundary conditions. Our result…

math.AP2012★ 36 cited

Finite-time blowup for a complex Ginzburg-Landau equation

Thierry Cazenave, Flávio Dickstein, Fred B. Weissler

We prove that negative energy solutions of the complex Ginzburg-Landau equation $e^{- i θ} u_{t} = Δ u + ∣ u ∣^{α} u$ blow up in finite time, where α>0 and π/2<θ<π/2. For a fixed initial val…

math.AP2012

Singularity formation and blowup of complex-valued solutions of the modified KdV equation

Jerry L. Bona, Stéphane Vento, Fred B. Weissler

The dynamics of the poles of the two--soliton solutions of the modified Korteweg--de Vries equation $u_{t} + 6 u^{2} u_{x} + u_{xxx} = 0$ are determined. A consequence of this study is…