The pressure equation for fluid flow in a stochastic medium

H. Holden; T. Lindstrøm; B. Øksendal; J. Ubøe; T. -S. Zhang

doi:10.1007/bf02345830

journal article Dec 01, 1995

The pressure equation for fluid flow in a stochastic medium

H. Holden T. Lindstrøm B. Øksendal J. Ubøe T. -S. Zhang

Potential Analysis Vol. 4 No. 6 pp. 655-674 · Springer Science and Business Media LLC

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References

25

[1]

S. Albeverio, Y. Kondratiev, and L. Streit: ‘Spaces of White Noise Distributions: Constructions, Descriptions, Applications II’, Manuscript 1993. 10.1016/0034-4877(93)90003-w

[2]

J. Ash and J. Potthoff: ‘Ito's Lemma without Non-Anticipatory Conditions’,Probab. Th. Rel. Fields 88 (1991), 17–46. 10.1007/bf01193581

[3]

F. E. Benth: ‘Integrals in the Hida Distribution Space (S)*, in T. Lindstrøm, B. Øksendal, and A. S. Ustunel (eds.),Stochastic Analysis and Related Topics, Gordon & Breach, 1993, pp. 89–99.

[4]

R. A. Carmona and J. A. Yan: ‘A New Space of White Noise Distributions and Applications to SPDE's’. Manuscript 1994. 10.1007/978-3-0348-7026-9_4

[5]

E. Dikow and U. Hornung: ‘A Random Boundary Value Problem Modelling Spatial Variability in Porous Media Flow,’ in M. F. Wheeler (ed),Numerical Simulation in Oil Recovery, IMA-Vol. II, Springer 1988, pp. 111–117. 10.1007/978-1-4684-6352-1_8

[6]

I. M. Gelfand and N. Y. Vilenkin:Generalized Functions, Vol. 4: Applications of Harmonic Analysis, Academic Press 1964 (English translation).

[7]

H. Gjessing: A note on the Wick product, Preprint, University of Bergen, 1993.

[8]

J. Gjerde: Multidimensional noise, Cand. Scient Thesis, Univ. of Oslo, 1993.

[9]

H. Gjessing, H. Holden, T. Lindstrøm, B. Øksendal, J. Ubøe, and T.-S. Zhang: ‘The Wick Product’, in H. Niemi, G. Högnäs, A. N. Shiryaev and A. Melnikov (eds),Frontiers in Pure and Applied Probability, Vol. 1. TVP Publishers, Moscow, 1993, pp. 29–67.

[10]

T. Hida:Brownian Motion, Springer-Verlag, 1980. 10.1007/978-1-4612-6030-1

[11]

T. Hida, H.-H. Kuo, J. Potthoff, and L. Streit:White Noise Analysis, Kluwer, 1993. 10.1007/978-94-017-3680-0

[12]

H. Holden, T. Lindstrøm, B. Øksendal, and J. Ubøe: ‘Discrete Wick Calculus and Stochastic Functional Equations’,Potential Analysis 1 (1992), 291–306. 10.1007/bf00269512

[13]

H. Holden, T. Lindstrøm, B. Øksendal, and J. Ubøe: ‘Discrete Wick Products’, in T. Lindstrøm, B. Øksendal and A. S. Ustunel (eds.),Stochastic Analysis and Related Topics, Gordon & Breach, 1993, pp. 123–148.

[14]

E. Hille and R. S. Phillips: ‘Functional Analysis and Semigroups’,Amer. Math. Soc. Colloq. Publ. 31 (1957).

[15]

H. Holden, T. Lindstrøm, B. Øksendal, J. Ubøe, and T.-S. Zhang: ‘Stochastic Boundary Value Problems: A White Noise Functional Approach’,Probab. Th. Rel. Fields 95 (1993), 391–419. 10.1007/bf01192171

[16]

H. Holden, T. Lindstrøm, B. Øksendal, J. Ubøe, and T.-S. Zhang: ‘The Burgers Equation with a Noisy Force’,Communications PDE 19 (1994), 119–141. 10.1080/03605309408821011

[17]

H. Holden, B. Øksendal, J. Ubøe, and T.-S. Zhang:Stochastic Partial Differential Equations (Forthcoming book).

[18]

T. Hida and J. Potthoff: ‘White Noise Analysis — an Overview’, in T. Hida, H.-H. Kuo, J. Potthoff, and L. Streit (eds.),White Noise Analysis, World Scientific, 1990. 10.1142/9789814540377

[19]

Y. Kondratiev, P. Leukert, and L. Streit: ‘Wick Calculus in Gaussian Analysis’, Manuscript 1994.

[20]

T. Lindstrøm, B. Øksendal, and J. Ubøe: ‘Stochastic Differential Equations Involving Positive Noise’, in M. Barlow and N. Bingham (eds.),Stochastic Analysis, Cambridge Univ. Press, 1991, pp. 261–303. 10.1017/cbo9780511662980.011

[21]

T. Lindstrøm, B. Øksendal, and J. Ubøe: ‘Wick Multiplication and Ito-Skorohod Stochastic Differential Equations’, in S. Albeverio et al. (eds.),Ideas and Methods in Mathematical Analysis, Stochastics, and Applications, Cambridge Univ. Press, 1992, pp. 183–206.

[22]

T. Lindstrøm, B. Øksendal, and J. Ubøe: ‘Stochastic Modelling of Fluid Flow in Porous Media’, in S. Chen and J. Yong (eds.),Control Theory, Stochastic Analysis and Applications, World Scientific, 1991, pp. 156–172.

[23]

O. Martio and B. Øksendal: ‘Fluid Flow in a Medium Distorted by Quasiconformal Map Can Produce Fractal Boundaries’, to appear inEuropean J. Applied Mathematics.

[24]

B. Øksendal:Stochastic Differential Equations, Springer-Verlag, 1992 (Third edition). 10.1007/978-3-662-02847-6

[25]

T.-S. Zhang: ‘Characterizations of White Noise Test Functions and Hida Distributions;Stochastics 41 (1992), 71–87.

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Published: Dec 01, 1995
Vol/Issue: 4(6)
Pages: 655-674
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Cite This Article

H. Holden, T. Lindstrøm, B. Øksendal, et al. (1995). The pressure equation for fluid flow in a stochastic medium. Potential Analysis, 4(6), 655-674. https://doi.org/10.1007/bf02345830

The pressure equation for fluid flow in a stochastic medium

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