Analysis and Applied Mathematics Seminar
Gustavo Ponce
University of California, Santa Barbara
On special regularity properties of solutions to a class of dispersive equations
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.
Monday March 28, 2016 at 4:00 PM in SEO 636