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SUMMARY:Probabilistic representation of a generalised porous media type eq
 uation: non-degenerate and degenerate cases - Russo\, F (INRIA Paris)
DTSTART:20100401T143000Z
DTEND:20100401T153000Z
UID:TALK23994@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider a porous media type equation (PME) over the real l
 ine  with monotone  discontinuous coefficient \nand prove a probabilistic 
 representation of its solution  in terms of an associated  microscopic dif
 fusion.\n\nWe will distinguish between two different situations: the so-ca
 lled {f non-degenerate} and {f degenerate}\ncases. In the first case we 
 show existence and uniqueness\, however in the second one for which we onl
 y show existence. One of the main analytic ingredients of the proof (in th
 e non-degerate case) is a new result\non uniqueness of distributional solu
 tions of a linear PDE on $R^1$ with non-continuous coefficients.\nIn the d
 egenerate case\, the proofs require a careful analysis of the deterministi
 c (PME) equation. \nSome comments about an associated stochastic  PDE with
  multiplicative noise will be provided.   \n\nThis talk is based partly on
  two joint papers: the first with  Ph. Blanchard and M. R"ockner\, the sec
 ond one with V. Barbu and M. R"ockner}.
LOCATION:Seminar Room 1\, Newton Institute
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