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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Probabilistic representation of a generalised poro
us media type equation: non-degenerate and degener
ate cases - Russo\, F (INRIA Paris)
DTSTART;TZID=Europe/London:20100401T153000
DTEND;TZID=Europe/London:20100401T163000
UID:TALK23994AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/23994
DESCRIPTION:We consider a porous media type equation (PME) ove
r the real line with monotone discontinuous coef
ficient \nand prove a probabilistic representation
of its solution in terms of an associated micro
scopic diffusion.\n\nWe will distinguish between t
wo different situations: the so-called {f non-deg
enerate} and {f degenerate}\ncases. In the first
case we show existence and uniqueness\, however in
the second one for which we only show existence.
One of the main analytic ingredients of the proof
(in the non-degerate case) is a new result\non uni
queness of distributional solutions of a linear PD
E on $R^1$ with non-continuous coefficients.\nIn t
he degenerate case\, the proofs require a careful
analysis of the deterministic (PME) equation. \nSo
me comments about an associated stochastic PDE wi
th multiplicative noise will be provided. \n\nTh
is talk is based partly on two joint papers: the f
irst with Ph. Blanchard and M. R"ockner\, the sec
ond one with V. Barbu and M. R"ockner}.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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