6 citations · 6 across the 2 of their papers we have counts for
11 papers
Asymptotic behavior for a dissipative nonlinear Schrödinger equation
Thierry Cazenave, Zheng Han, Ivan Naumkin
We consider the Schrödinger equation with nonlinear dissipation \begin{equation*} i \partial _t u +Δu=λ|u|^αu \end{equation*} in , , where $λ\in {\mathbb C}…
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 on , , with , where…
Local smooth solutions of the nonlinear Klein-gordon equation
Thierry Cazenave, Ivan Naumkin
Given any and , we prove the local existence of arbitrarily smooth solutions of the nonlinear Klein-Gordon equation $\partial_{ tt } u - Δu + μ_1 u =…
Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation
Thierry Cazenave, Zheng Han
We study the time-asymptotic behavior of solutions of the Schrödinger equation with nonlinear dissipation \begin{equation*} \partial _t u = i Δu + λ|u|^αu \end{equation*} in ${\mat…
Blowup on an arbitrary compact set for a Schödinger equation with nonlinear source term
Thierry Cazenave, Zheng Han, Yvan Martel
We consider the nonlinear Schrödinger equation on , , \begin{equation*} \partial _t u = i Δu + λ| u |^αu \quad \mbox{on , ,} \end{equat…
Solutions with prescribed local blow-up surface for the nonlinear wave equation
Thierry Cazenave, Yvan Martel, Lifeng Zhao
We prove that any sufficiently differentiable space-like hypersurface of coincides locally around any of its points with the blow-up surface of a finite-energy…