Steady and self-similar solutions to systems of two-dimensional conservation laws.

Hyperbolic and Mixed Type PDEs Seminar

Meeting Details

For more information about this meeting, contact Stephanie Geyer.

Speaker: Joe Roberts, Penn State

Abstract: We consider solutions to systems of 2D conservation laws that are steady in time and constant along rays emanating from the origin. This reduction is inspired by problems in shock wave reflection for the compressible Euler equations, in which the flow is locally well described by solutions with these symmetry properties. For general systems with genuinely nonlinear or linearly degenerate characteristic fields of constant multiplicity, we prove any admissible $L^\infty$ solution that is a small perturbation of a constant state is necessarily a special function of bounded variation. In addition, we describe the possible configurations of different kinds of waves, and show that they are what we intuitively expect. How this answers some questions and improves known results regarding uniqueness (forward in time) and regularity (more interesting for backward in time) for one-dimensional Riemann problems will also be discussed.

Room Reservation Information

Room Number: 216 McAllister

Date: 09/19/2013

Time: 10:00am - 10:50am