Stability of Solutions of Parabolic PDEs with Random Drift and Viscosity Limit |
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Authors: | T Deck J Potthoff G Våge H Watanabe |
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Institution: | (1) Lehrstuhl für Mathematik V, University of Mannheim, D-68131 Mannheim, Germany , DE;(2) Department of Applied Mathematics, Faculty of Science, Okayama University of Science, Okayama, Japan, JP |
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Abstract: | Let u
α
be the solution of the It? stochastic parabolic Cauchy problem , where ξ is a space—time noise. We prove that u
α
depends continuously on α , when the coefficients in L
α
converge to those in L
0
. This result is used to study the diffusion limit for the Cauchy problem in the Stratonovich sense: when the coefficients
of L
α
tend to 0 the corresponding solutions u
α
converge to the solution u
0
of the degenerate Cauchy problem . These results are based on a criterion for the existence of strong limits in the space of Hida distributions (S)
*
. As a by-product it is proved that weak solutions of the above Cauchy problem are in fact strong solutions.
Accepted 22 May 1998 |
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Keywords: | , Stochastic partial differential equations, White noise analysis, Turbulent transport equation, Viscosity limit,,,,,,AMS Classification, 60H15, 60G20, |
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