Existence and Stability of Traveling Waves for an Integro-differential Equation for Slow Erosion

Hyperbolic and Mixed Type PDEs Seminar

Meeting Details

For more information about this meeting, contact Stephanie Zerby.

Speaker: Wen Shen, Penn State

Abstract: We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique traveling wave solutions that connect profiles with equilibrium slope at $\pm\infty$. Such traveling waves take very different forms from those in standard conservation laws. Furthermore, we prove that the traveling wave profiles are locally stable, i.e., solutions with monotone initial data approaches the traveling waves asymptotically as $t\to+\infty$.

Room Reservation Information

Room Number: 216 McAllister

Date: 04/04/2013

Time: 10:00am - 10:50am