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A weak space-time formulation for the linear stochastic heat equation

Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Matteo Molteni (Institutionen för matematiska vetenskaper, matematik)

We apply the well-known Banach-Necas-Babuska inf-sup theory in a stochastic setting to introduce a weak space-time formulation of the linear stochastic heat equation with additive noise. We give sufficient conditions on the the data and on the covariance operator associated to the driving Wiener process, in order to have existence and uniqueness of the solution. We show the relation of the obtained solution to the so-called mild solution and to the variational solution of the same problem. The spatial regularity of the solution is also discussed. Finally, an extension to the case of linear multiplicative noise is presented.

Nyckelord: Inf-sup theory, Stochastic linear heat equation, Additive noise, Linear multiplicative noise

Denna post skapades 2014-03-07. Senast ändrad 2016-03-22.
CPL Pubid: 194649


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Numerisk analys

Chalmers infrastruktur

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A weak space-time formulation for the linear stochastic heat equation