Stability of Solutions of Parabolic PDEs with Random Drift and Viscosity Limit
- Lehrstuhl fuer Mathematik V, University of Mannheim, D-68131 Mannheim (Germany)
- Department of Applied Mathematics, Faculty of Science, Okayama University of Science, Okayama (Japan)
Let u{sub {alpha}} be the solution of the Ito stochastic parabolic Cauchy problem {partial_derivative}u/{partial_derivative}t - L{sub ={xi}}{sub .{nabla}}{sub u,u} , where {xi} is a space-time noise. We prove that u{sub {alpha}} depends continuously on {alpha} , when the coefficients in L{sub {alpha}} converge to those in L{sub 0} . This result is used to study the diffusion limit for the Cauchy problem in the Stratonovich sense: when the coefficients of L{sub {alpha}} tend to 0 the corresponding solutions u{sub {alpha}} converge to the solution u{sub 0} of the degenerate Cauchy problem {partial_derivative}u{sub 0}/{partial_derivative}t={xi} o {nabla}u{sub 0}, u{sub o} . These results are based on a criterion for the existence of strong limits in the space of Hida distributions (S){sup *} . As a by-product it is proved that weak solutions of the above Cauchy problem are in fact strong solutions.
- OSTI ID:
- 21064280
- Journal Information:
- Applied Mathematics and Optimization, Vol. 40, Issue 3; Other Information: DOI: 10.1007/s002459900132; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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