##### Department of Mathematics,

University of California San Diego

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### Math 248 - Real Analysis

## Gautam Iyer

#### Carnegie Mellon

## Anomalous diffusion in one and two dimensional combs

##### Abstract:

We study the effective behavior of a Brownian motion in both one and two dimensional comb like domains. This problem arises in a variety of physical situations such as transport in tissues, and linear porous media. We show convergence to a limiting process when when both the spacing between the teeth, and the probability of entering a tooth vanish at the same rate. This limiting process exhibits an anomalous diffusive behavior, and can be described as a Brownian motion time-changed by the local time of an independent sticky Brownian motion. At the PDE level, this leads to equations that have fractional time derivatives and are similar to the Bassett differential equation.

Host: Andrej Zlatos

### May 30, 2019

### 11:00 AM

### AP&M 7321

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