Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 19.11.2015 at 14:00 Lecture room M-223

Tatsuki Kawakami (Osaka Prefecture University a Universita degli Studi di Milano):

Existence of mild solutions for the Hamilton-Jacobi equation

with critical fractional viscosity in the Besov spaces

Abstract:

We consider the Cauchy problem for the Hamilton-Jacobi equation with critical dissipation.

We show that for sufficiently small initial data, there exists a global-in-time mild solution.

Furthermore, we prove that the solution behaves asymptotically like a suitable multiple

of the Poisson kernel.

This talk is based on a joint work with Tsukasa Iwabuchi (Osaka city University, Japan).