Tel Aviv University, Applied Mathematics Seminar
 
Date:       Tuesday December 18, 2012, 15:10
 
Place:      Schreiber Bldg, Room 309
 
Speaker: Michael Sever, Hebrew University
 
Title: A Continuation of weak solutions of hyperbolic systems of
conservation laws
 
Abstract:
 
An argument, well short of a complete proof, is given that the Cauchy
problem for nonlinear, hyperbolic systems of conservation laws in
more than one space dimension and time, is in general not well posed.
 
Consideration of continuation of weak solutions of a simple form as
the initial data is varied leads to a seemingly necessary estimate on
the space of test functions determining the weak solution. Attempt to
obtain such an estimate is seen to require an admissibility condition
on discontinuities.
 
We postulate such an admissibility condition. In one space dimension,
familiar conditions are recovered, but in general the condition
cannot be expected in higher dimensions. Nonetheless, we show that
shocks can be admissible in this sense for reduced, relativistic
Euler systems.
 
Webpage of the applied mathematics seminar:
 <https://sites.google.com/site/tauamathseminar/>
 
______________________________________________________________________
 
Dr. Yoel Shkolnisky
Department of Applied Mathematics
School of Mathematical Sciences        phone:  972-3-640-8705
Tel Aviv University,                   fax  :  972-3-640-9357
Tel Aviv, 69978 Israel                 email:   <yoelsh@post.tau.ac.il>
______________________________________________________________________
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Yoel Shkolnisky   <yoelsh@post.tau.ac.il>