07/09/2016, 09:40 — 10:20 — Amphitheatre Pa2, Mathematics Building
João Paulo Dias, Universidade de Lisboa

On a quasilinear non-local Benney system

We consider the quasilinear non-local Benney system

\[ \begin{cases}i u_t + u_{xx} = |u|^2 u + buv \\ \displaystyle v_t + a \left( \int_{\mathbb{R}^+} v^2 \ dx \right) v_x = -b(|u|^2)_x , \quad (x,t) \in \mathbb{R}^+ \times [0,\infty[ . \end{cases} \]

We study the existence and uniqueness of the local strong solutions to the initial boundary value problem, their possible blowup, the existence of global weak solutions and we exhibit bound-state solutions in some special cases.This talk is based on a submitted paper by J. P. Dias and F. Oliveira with the same title.