Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 26.10.2017 at 14:00 Lecture room M-223

Hannes Stuke (Freie Universitaet Berlin):

Complex time blow-up in parabolic differential equations

Abstract:

In my talk I want to study blow-up in partial differential equations

from the perspective of complex time. The main example will be

the semilinear heat equation $u_t = u_{xx} + u^2$

on a bounded or unbounded interval. For real $u, x$ and real time $t$,

this equation has already been well-studied in the literature.

It has been shown, that solutions can blow-up in finite time.

Bounded solutions are analytic in time and admit

an analytic continuation into the complex plane.

Following an idea of Masuda and Guo et al.,

I construct the extensions of solutions to complex time

and study their properties. Building up on that example,

I want to further examine the hidden kinship between

bounded solutions and blow-up in parabolic differential equations.