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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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