Gustavo Ponce : On special regularity properties of solutions to a class of dispersive equations

Posted by Christof Sparber , part of the Analysis and Applied Mathematics Seminar.

At

March 28, 2016, 4 p.m.

In

SEO 636

Abstract

In a joint work with P. Isaza and F. Linares we show that solutions of the IVP for the $k$-generalized KdV equation \begin{equation} \begin{cases} \begin{aligned} \label{aaa} &\partial_t u + \partial_x^3 u +u^k\partial_x u=0,\;\;\;\;\;t,\;x\in\mathbb R,\;\;k\in\mathbb Z^+,\\ &u(x,0)=u_0(x) \end{aligned} \end{cases} \end{equation} preserve some smoothness of the initial data $u_0$ and that this regularity moves with infinite speed to its left as time evolves.