Summer 2004 PDEs

We study the formation and evolution of shockwaves from initial data given nonlinear hyperbolic systems of partial differential equations. Our emphasis is on the Riemann problem starting from a point in statespace; what states can be connected to a given state given a flux function? How do Lie Brackets measure the effects of a wave interaction? It is our goal to compute the relevant information for multiple hyperbolic systems and to represent the systems graphically.

We first state our main results then give the chronological development of our ideas and knowledge of subject matter. It is hoped that by sharing our main results, we can be of some service to those working in the field. We further hope that the chronology might be of some use to undergraduates studying NLPDEs..

Our main results: Unified Analyzer and Physical Systems

Week <1: Introduction to Conservation Laws

Week 1: 6/14 Rankine Hugoniot Locus, Euler, Napier and Burger

Week 2: 6/21 State Space.

Week 3: 6/28 Systems I Ahat, P System, Elastic String

Week 4: 7/5 Systems II Euler Gas Dynamics, Maxwell's equaitons

Week 5: 7/12 Update

Week 6: 7/19 Interpretation of Eigensystem

Week 7: 7/26 Lie Brackets, Coupling and Riemann Invarients

Week 8: 8/2 Literature Review

Week 9: 8/9 Interaction coefficients

Week 10: 8/16 Wrap up

Bibliography: The books we've studied

About Us: Pat, Robin and Rob