Seminar on Qualitative Theory of Differential Equations - Hennes Stuke (26.10.2017)
Thursday 26.10.2017 at 14:00 hod., Lecture room M/223
Hannes Stuke (Freie Universität 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.