ISSN:
1432-0606
Keywords:
Key words. Stochastic partial differential equations, White noise analysis, Turbulent transport equation, Viscosity limit. AMS Classification. 60H15, 60G20.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. Let u α be the solution of the Itô stochastic parabolic Cauchy problem $\partial u/\partial t-L_\a u = \xi \cdot \nabla u, \ u\v_{t=0} = f$ , 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 $\partial u_0/ \partial t =\xi\circ \nabla u_0, \ u_0\v_{t=0} = f$ . 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002459900132
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