Seminar 26.10.2017: Hannes Stuke

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 26.10.2017: Hannes Stuke

Postby quittner » Fri Oct 20, 2017 9:51 am

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

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.
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