Procedure of announcing a seminar

Step 1:

Please first fix the time and then ask for Madame Blanchard to book a room.

Step 2:

Please fill the following form:

# Personal Title: Prof.

# Name: Daniel Conus

# Homepage:

# Affiliation: University of Utah

# Chair: Probability

# Seminar Title: On the chaotic character of the stochastic heat equation, before the onset of intermitttency

# Date: Thursday, 16th December

# Time: from 11h15 to 12h15

# Room: MAA 112

# Inviter: Robert Dalang

# Abstract:

We consider a nonlinear stochastic heat heat equation $\partial_t u = \frac12 \partial_{xx} u + \sigma(u)\partial_{xt}W$, where $\partial_{xt}W$ denotes space-time white noise and $\sigma:\mathbb{R}\to\mathbb{R}$ is Lipschitz continuous. We establish that, at every fixed time $t>0$, the global behavior of the solution depends in a critical manner on the structure of the initial function $u_0$. Under suitable technical conditions on $u_0$ and $\sigma$, $\sup_{|x|\le R}u_t(x)$ remains bounded in $R$ when $u_0$ has compact support, whereas with probability one, $\sup_{|x|\le R}u_t(x)\ge\text{const}\cdot (\log R)^{1/6}$ as $R\to\infty$ when $u_0$ is bounded uniformly away from zero. The mentioned sensitivity to the initial data of the stochastic heat equation is a way to state that the solution to the stochastic heat equation is chaotic at fixed times, well before the onset of intermittency.

This is a joint work with Davar Khoshnevisan and Mathew Joseph, University of Utah.

Here are some more sample files: 1, 2, 3.

Note that in the “Abstract” part, simple Latex commands are supported by MathJax. See for example Prof. Conus’s seminar and his file.

Step 3:

Send the above form to David Candil, by either copy-pasting the above form in the email or attaching the form as an independent file. Thanks.