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SUMMARY:On a well-tempered diffusion - Philip Rosenau (Tel Aviv University
 )
DTSTART:20130613T140000Z
DTEND:20130613T150000Z
UID:TALK40694@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:The classical transport theory as expressed by\, say\, the Fok
 ker-Planck equation\, lives in an analytical paradise but\, in sin. Not on
 ly its response to initial datum spreads at once everywhere oblivious of t
 he basic tenets of physics\, but it also induces an infinite flux across a
  sharp interface. Attempting to overcome these difficulties one notices th
 at the moment expansion of any of the micro ensembles of the kind that beg
 et the equations of the classical mathematical physics\, say the Chapman-E
 nskog expansion of Boltzmann Eq.\, if extended beyond the second moment\, 
 yields an ill posed PDE (the Pawla Paradox)!  \n\nWe shall describe mathem
 atical strategies to overcome these generic difficulties. The resulting fl
 ux-limited transport equations are well posed and capture some of the cruc
 ial effects of the original ensemble lost in moment expansion. For instanc
 e\, initial discontinuities do not dissolve at once but persist for a whil
 e. There is a critical transition from analytical to discontinuous states 
 with embedded sub-shock(s). 
LOCATION:MR 14\, CMS
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