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Foundations Of Nonstandard Analysis  A Gentle Introduction to Nonstandard Extemsions
 In Nonstandard analysis (Edinburgh
"... this paper is to describe the essential features of the resulting frameworks without getting bogged down in technicalities of formal logic and without becoming dependent on an explicit construction of a specific field ..."
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Cited by 10 (2 self)
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this paper is to describe the essential features of the resulting frameworks without getting bogged down in technicalities of formal logic and without becoming dependent on an explicit construction of a specific field
A two space dimensional semilinear heat equation perturbed by (Gaussian) white noise
, 1999
"... A twospace dimensional heat equation perturbed by a white noise driven in a bounded volume is considered. The equation is perturbed by a nonlinearity of the type : f(AU) :, where : : means Wick (re)ordering with respect to the free solution; ; A are small parameters, U denotes a solution, f is t ..."
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Cited by 3 (0 self)
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A twospace dimensional heat equation perturbed by a white noise driven in a bounded volume is considered. The equation is perturbed by a nonlinearity of the type : f(AU) :, where : : means Wick (re)ordering with respect to the free solution; ; A are small parameters, U denotes a solution, f is the Fourier transform of a complex measure with compact support. Existence and uniqueness of the solution in a class of ColombeauOberguggenberger generalized functions is proven. An explicit construction of the solution is given and it is shown that each term of the expansion in a power series in is associated with an L 2 valued measure when A is a small enough. AMS CLASSIFICATION (1985) Primary: 60H15 Secondary: 35D05 35K22 35K55 35Q99 KEYWORDS: Stochastical partial differential equations, random generalized functions, parabolic type, stochastic quantization (of SineGordon equation) (1) Institut fur Angewandte Mathematik, Wegelerstr. 6, D53155 Bonn (Germany) (4) Universitat Biel...
Measure Attractors For Stochastic NavierStokes Equations
, 1998
"... : We show existence of measure attractors for 2D stochastic NavierStokes equations with general multiplicative noise. Keywords: Stochastic NavierStokes equations, measure attractors AMS subject classification: Primary: 35Q30, 60H15, 60G60; Secondary: 35R60, 76D05, 60J25 The research of the firs ..."
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: We show existence of measure attractors for 2D stochastic NavierStokes equations with general multiplicative noise. Keywords: Stochastic NavierStokes equations, measure attractors AMS subject classification: Primary: 35Q30, 60H15, 60G60; Secondary: 35R60, 76D05, 60J25 The research of the first author was supported by an EPSRC Visiting Fellowship at the University of Hull and also partially by the KBN grant 2PO3A 064 08. Submitted to EJP on 15 May, 1997. Final version accepted on May 20, 1998. MEASURE ATTRACTORS FOR STOCHASTIC NAVIERSTOKES EQUATIONS MAREK CAPI ' NSKI AND NIGEL J. CUTLAND Abstract. We show existence of measure attractors for 2D stochastic NavierStokes equations with general multiplicative noise. 1. Introduction This paper is concerned with existence of attractors in connection with stochastic NavierStokes equations in dimension 2. For deterministic NavierStokes equations, the existence of a global attractor in dimension 2 goes back to the work of Ladyzh...
Journal of Applied Mathematics and Stochastic Analysis, 13:3 (2000), 239259. GALERKIN APPROXIMATION AND THE STRONG SOLUTION OF THE NAVIERSTOKES EQUATION
, 1999
"... We consider a stochastic equation of NavierStokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square. ..."
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We consider a stochastic equation of NavierStokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.