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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Stochastic variational inequalities and applicatio
ns to the total variation flow pertubed by linear
multiplicative noise - Rckner\, M (Universitt Biel
efeld)
DTSTART;TZID=Europe/London:20120914T095000
DTEND;TZID=Europe/London:20120914T104000
UID:TALK39749AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39749
DESCRIPTION:We extend the approach of variational inequalities
(VI) to partial differential equations (PDE) with
singular coefficients\, to the stochastic case. A
s a model case we concentrate on the parabolic 1-L
aplace equation (a PDE with highly singular diffus
ivity) on a bounded convex domain in N-dimensional
Euclidean space\, perturbed by linear multiplicat
ive noise\, where the latter is given by a functio
n valued (infinite dimensional) Wiener process. We
prove existence and uniqueness of solutions for t
he corresponding stochastic variational inequality
(SVI) in all space dimensions N and for any squar
e-integrable initial condition\, thus obtaining a
stochastic version of the (minimal) total variatio
n flow. One main tool to achieve this\, is to tran
sform the SVI and its approximating stochastic PDE
into a deterministic VI\, PDE respectively\, with
random coefficients\, thus gaining sharper spatia
l regularity results for the solutions. We also pr
ove finite time extinction of solutions with posit
ive probability in up to N = 3 space dimensions.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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