Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 4.3.2021 at 14:00

Marek Fila (KAMŠ FMFI UK):

Solutions with snaking singularities for the fast diffusion equation

MS-teams link:

https://teams.microsoft.com/l/meetup-jo ... afe3%22%7d

Abstract:

We construct solutions of the fast diffusion equation, which exist for all $t\in\R$ and are singular on the set

$\Gamma(t):= \{ \xi(s) ; -\infty <s \leq ct \}$, $c>0$, where $\xi\in C^3(\R;\R^n)$, $n\geq 2$.

We also give a precise description of the behavior of the solutions near $\Gamma(t)$.

This is a joint work with John King, Jin Takahashi and Eiji Yanagida.