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Generalized solution of some parabolic equations with a random drift

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Abstract

Some stochastic partial differential equations arising from a turbulent transport model are studied using Hida's theory of Brownian functionals. For the spatially homogeneous case, the solutions are constructed as a regular or generalized Brownian functional, depending on a small parameter. The regularity property of such solutions is also determined. However, for the spatially nonhomogeneous equations, only generalized solutions in a series form involving iterated singular Wiener integrals are found.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, 48202, Detroit, MI, USA

    Pao-Liu Chow

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  1. Pao-Liu Chow
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Additional information

This work was supported in part by NSF Grant DMS-87-02236.

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Chow, PL. Generalized solution of some parabolic equations with a random drift. Appl Math Optim 20, 1–17 (1989). https://doi.org/10.1007/BF01447642

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  • DOI: https://doi.org/10.1007/BF01447642

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