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Dostęp zamkniętyLp solutions for a stochastic evolution equation with nonlinear potential
| dc.abstract.en | This article deals with the stochastic partial differential equation ⎧⎩⎨ut=12uxx+uγξ,u(0,⋅)=u0, where ξ is a space/time white noise Gaussian random field, γ∈(1,∞) and the initial condition u0 is a non-negative measurable mapping, independent of ξ satisfying u0≥0 and additional conditions given in the article. The space variable is x∈S1=[0,1] with the identification 0=1. The definition of the stochastic term, taken in the sense of Walsh, will be made clear in the article. The result is that there exists a non-negative solution u such that for all α∈[0,1), E[(∫∞0∫S1u(t,x)2γdxdt)α/2]≤K(α)E[(∫S1u0(x)dx)α]<∞. where the finite constant K(α) is derived from the Burkholder–Davis–Gundy inequality constants. The solution is unique among solutions which satisfy this. Solutions are also shown to satisfy E[∫T0(∫S1u(t,x)pdx)α/pdt]<∞ ∀T<∞,0<p<∞,α∈(0,1/2). |
| dc.affiliation | Uniwersytet Warszawski |
| dc.contributor.author | Noble, John |
| dc.date.accessioned | 2024-01-25T05:29:42Z |
| dc.date.available | 2024-01-25T05:29:42Z |
| dc.date.issued | 2022 |
| dc.description.finance | Publikacja bezkosztowa |
| dc.description.number | 2 |
| dc.description.volume | 264 |
| dc.identifier.doi | 10.4064/SM210120-2-9 |
| dc.identifier.issn | 0039-3223 |
| dc.identifier.uri | https://repozytorium.uw.edu.pl//handle/item/111580 |
| dc.identifier.weblink | http://dx.doi.org/10.4064/sm210120-2-9 |
| dc.language | eng |
| dc.pbn.affiliation | mathemathics |
| dc.relation.ispartof | Studia Mathematica |
| dc.relation.pages | 181-240 |
| dc.rights | ClosedAccess |
| dc.sciencecloud | nosend |
| dc.title | Lp solutions for a stochastic evolution equation with nonlinear potential |
| dc.type | JournalArticle |
| dspace.entity.type | Publication |