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An Introduction to the Mathematical Theory of Shock Waves and Conservation Laws
Student-Run Research| Speaker: | Brian Wissman, UC Davis |
| Location: | 2112 MSB |
| Start time: | Wed, Mar 14 2007, 12:10PM |
Description
Shock waves are physical phenomena that occur in flows past
supersonic jets, blast waves, traffic flow, super-nova and gamma-ray bursts.
These waves arise naturally in the mathematical theory of non-linear
conservation laws where non-linearities produce shocks by allowing waves to
"break." More specifically, shock waves result from the finite time blowup
of the regularity of one or more conserved quantities.
In 1965 Glimm proved existence of solutions to general systems of conservation laws. This generality came at a cost, however, because our initial data must be restricted. In this talk I will give an introduction to the mathematical theory of shock waves and outline Glimm's method for proving existence of shock wave
solutions to systems of conservation laws. We will also discuss how the
particular structure of the Ultra-Relativistic Euler Equations, a system of
conservation laws, allows one to improve upon Glimm's existence result.