Event Type:

Analysis Seminar

Date/Time:

Monday, November 13, 2017 - 12:00 to 13:00

Location:

Gilkey 104

Guest Speaker:

Abstract:

We consider the two initial value problems $u^\prime(t) = -u(t) + u^2(\alpha t), u(0) = u_0\in\{0,1\},$ where $\alpha > 0$ is a fixed parameter. The equation arose as a mean-field version of mild (Fourier transformed) equations arising in fluids. Existence is clearly resolved by constant solutions in the cases $u_0\in \{0,1\}$, so the problem to be analyzed is that of uniqueness. The question is resolved in terms of explosion probabilities for an associated branching random walk. This is based on joint work with Radu Dascaliuc, Nicholas Michalowski, and Enrique Thomann