A STOCHASTIC PARABOLIC EQUATION WITH NONLINEAR FLUX ON THE BOUNDARY DRIVEN BY A GAUSSIAN NOISE

作者：Barbu Viorel^*; Bonaccorsi Stefano; Tubaro Luciano

来源：SIAM Journal on Mathematical Analysis, 2014, 46(1): 780-802.

DOI：10.1137/130924822

• nonlinear heat diffusion
• stochastic boundary conditions
• Brownian motion
• fractional Brownian motion

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.

• 出版日期2014