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Chaos expansion of heat equations with white noise potentials
Hu, Yaozhong
Hu, Yaozhong
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Abstract
The asymptotic behavior as t --> infinity of the solution to the following stochastic heat equations [GRAPHICS] is investigated, where w is a space-time white noise or a space white noise. The use of lozenge means that the stochastic integral of 10 (Skorohod) type is considered. When d = 1, the exact L-2 Lyapunov exponents of the solution are studied. When the noise is space white and when d < 4 it is shown that the solution is in some "flat" L-2 distribution spaces. The Lyapunov exponents of the solution in these spaces are also estimated. The exact rate of convergence of the solution by its first finite chaos terms are also obtained.
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Date
2002-02
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KLUWER ACADEMIC PUBL
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pp_whitechaos.pdf
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Keywords
Chaos expansion, Space-time white noise potential, Space white noise potential, Stochastic heat equation, Lyapunov exponent, Mittag-leffler functions, Inite chaos approximation, Exact rate of convergence
Citation
Hu, YZ. Chaos expansion of heat equations with white noise potentials. POTENTIAL ANALYSIS. Feb 2002. 16(1). 45-66