Walter Rusin
Consider a system of first order PDEs of the form u_t + F(u)_x =0 with some initial condition u=g at t=0, where F: R^m -> R^m and g: R -> R^m are given and u:R x (0,+\infty) is the unknown. This kind of systems are known as conservation laws and show up quite often in physics (for instance the mixing of two gases separated initially by a membrane can be described that way). Riemann's problem is the initial value problem (IVP) for such system with initial data given as some state u_l for x<0 and another state u_r for x>0 (again: gases...). The purpose of the talk is to present some basic results and ideas related to that problem. No advanced knowledge in PDEs is assumed and these, by now classical, results will be fairly accessible to anybody who knows what a matrix or an eigenvalue is!
Go Back to Junior Coll. Web page
URL http://www.math.umn.edu/jrcoll/ The University of Minnesota is an equal opportunity educator and employer. © 2004, The Regents of the University of Minnesota |
|