F. Dickstein

activity

20122020

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

36 citations · 90 across the 8 of their papers we have counts for

collaborators

8 papers

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.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★ 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★ 5 cited

Sign-changing stationary solutions and blowup for the nonlinear heat equation in dimension two

Flavio Dickstrein, Filomena Pacella, Berardino Scunzi

Consider the nonlinear heat equation v_t-Δv=|v|^{p-1}v in the unit ball of R^2, with Dirichlet boundary condition. Let u_{p,K} be a radially symmetric, sign-changing stationary sol…

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…