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Mathematics Colloquium

Mark Hoefer
University of Colorado at Boulder

Title: Dispersive regularization of conservation laws: the mathematics and physics of nonlinear waves in dispersive media
Date: Friday, March 6, 2020
Place and Time: Room 101, Love Building, 3:35-4:25 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. Dispersive hydrodynamics-modeled by hyperbolic conservation laws subject to conservative, dispersive perturbation-has emerged as a unified mathematical framework for the description of multiscale nonlinear wave phenomena in dispersive media. It accurately describes a plethora of physical systems from geophysical fluids to condensed matter and intense laser light. One of the most prominent multiscale solutions in dispersive hydrodynamics is the dispersive shock wave that emerges from dispersive regularization of gradient catastrophe. Combining modeling, asymptotic analysis, numerical simulation, and experiment, this talk will highlight how the choice of dispersive regularization has a strong impact on the nature of dispersive shock waves. Example applications to viscous Stokes fluids, shallow water wave models, and ultracold atomic gases will be used to explore some counterintuitive effects such as the existence of expansion shocks to the generation of viscous shock waves in a conservative medium.