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- W2000616663 abstract "A two-space dimensional heat equation perturbed by a white noise in a bounded volume is considered. The equation is perturbed by a non-linearity of the type λ : f(AU) :, where :: means Wick (re)ordering with respect to the free solution;λ, 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 Colombeau-Oberguggenberger 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 λ is associated with an L 2-valued measure when A is a small enough." @default.
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- W2000616663 date "2001-11-01" @default.
- W2000616663 modified "2023-10-03" @default.
- W2000616663 title "A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise" @default.
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- W2000616663 doi "https://doi.org/10.1007/s004400100153" @default.
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