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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)
International Journal of Applied and Computational Mathematics (2349-5103). Vol. Epub ahead of print (2016),
[Artikel, refereegranskad vetenskaplig]

We apply the well-known Banach–Nečas–Babuška 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 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 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 2016-01-24. Senast ändrad 2016-03-22.
CPL Pubid: 231172

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik
Tillämpad matematik
Sannolikhetsteori och statistik

Chalmers infrastruktur