F. Dickstein

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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.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…