A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise |
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Authors: | Sergio Albeverio Zbignew Haba Francesco Russo |
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Institution: | (1) Institut für Angewandte Mathematik, Wegelerstrasse 6, D-53155 Bonn, Germany., DE;(2) Institute of Theoretical Physics, University of Wroclaw, Wroclaw, Poland., PL;(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 |
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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.
Received: 20 July 1997 / Revised version: 1 February 2001 / Published online: 9 October 2001 |
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