Fakulta matematiky, fyziky
a informatiky
Univerzita Komenského v Bratislave

Seminár z kvalitatívnej teórie diferenciálnych rovníc - Hennes Stuke (26.10.2017)

vo štvrtok 26.10.2017 o 14:00 hod. v miestnosti M/223


22. 10. 2017 20.49 hod.
Od: Pavol Quittner

Prednášajúci: Hannes Stuke (Freie Universität Berlin) 

Názov prednášky: Complex time blow-up in parabolic differential equations

Termín: 26.10.2017, 14:00 hod., M/223


Abstrakt:

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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