This paper concerns a class of stochastic parabolic equations with nonlinear boundary conditions and boundary noise, which is either a Wiener process or a fractional Brownian motion with Hurst parameter H > 1/2. Boundary degeneracy of the solution is already known in the literature; we show that in our framework we can overcome this difficulty and treat a nonlinear perturbation term on the boundary. The boundary nonlinear term is either Lipschitz continuous or a maximal monotone mapping.
A STOCHASTIC PARABOLIC EQUATION WITH NONLINEAR FLUX ON THE BOUNDARY DRIVEN BY A GAUSSIAN NOISE
Barbu, Viorel;Bonaccorsi, Stefano;Tubaro, Luciano
2014-01-01
Abstract
This paper concerns a class of stochastic parabolic equations with nonlinear boundary conditions and boundary noise, which is either a Wiener process or a fractional Brownian motion with Hurst parameter H > 1/2. Boundary degeneracy of the solution is already known in the literature; we show that in our framework we can overcome this difficulty and treat a nonlinear perturbation term on the boundary. The boundary nonlinear term is either Lipschitz continuous or a maximal monotone mapping.File in questo prodotto:
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