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• W3048330135 abstract "We consider the Cauchy problem for stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators. We adapt the notion of stochastic entropy solution and provide new technical framework to prove the uniqueness. The existence proof relies on the vanishing viscosity method. Moreover, using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence estimate on the nonlinearities and derive error estimate for the stochastic vanishing viscosity method. In addition, we develop uniqueness method a la Kruzkov for more general equations where the noise coefficient may depends explicitly on the spatial variable." @default.
• W3048330135 created "2020-08-13" @default.
• W3048330135 creator A5002154131 @default.
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• W3048330135 date "2020-08-06" @default.
• W3048330135 modified "2023-09-25" @default.
• W3048330135 title "A fractional degenerate parabolic-hyperbolic Cauchy problem with noise" @default.
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• W3048330135 hasPublicationYear "2020" @default.
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