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.
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Received: 20 July 1997 / Revised version: 1 February 2001 / Published online: 9 October 2001
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Albeverio, S., Haba, Z. & Russo, F. A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise. Probab Theory Relat Fields 121, 319–366 (2001). https://doi.org/10.1007/s004400100153
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DOI: https://doi.org/10.1007/s004400100153
Keywords
- Fourier
- Fourier Transform
- Generalize Function
- White Noise
- Power Series