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A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise
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  • Published: November 2001

A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise

  • Sergio Albeverio1,
  • Zbignew Haba2 &
  • Francesco Russo3 

Probability Theory and Related Fields volume 121, pages 319–366 (2001)Cite this article

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  • 24 Citations

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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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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Wegelerstrasse 6, D-53155 Bonn, Germany., , , , , , DE

    Sergio Albeverio

  2. Institute of Theoretical Physics, University of Wroclaw, Wroclaw, Poland., , , , , , PL

    Zbignew Haba

  3. Université Paris 13, Département de Mathématiques, Institut Galilée, avenue Jean Baptiste Clément, F-93400 Villetaneuse, France. e-mail: russo@math.univ-paris13.fr, , , , , , FR

    Francesco Russo

Authors
  1. Sergio Albeverio
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  2. Zbignew Haba
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  3. Francesco Russo
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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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  • Issue Date: November 2001

  • DOI: https://doi.org/10.1007/s004400100153

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Keywords

  • Fourier
  • Fourier Transform
  • Generalize Function
  • White Noise
  • Power Series
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