Homogenization of reflected semilinear PDE with nonlinear Neumann boundary condition

2007/12/18 by Auguste Aman, Aman, Auguste, Modeste N’zi +2
Computer Science · Engineering · Mathematics · #60H05 #60H20 #60H30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60H05 #msc:60H20 #msc:60H30

paper · pdf · doi:10.48550/arxiv.0712.2986

Ce papier a 19 pages et est soumis pour publication dans Stochastic Analysis and Applications

openalex publication_date 2007/12/18 · arxiv created 2009/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the homogenization problem of semi linear reflected partial differential equations (reflected PDEs for short) with nonlinear Neumann conditions. The non-linear term is a function of the solution but not of its gradient. The proof are fully probabilistic and uses weak convergence of associated reflected generalized backward differential stochastic equations (reflected GBSDEs in short).

Related

• Penalization of Reflected SDEs and Neumann Problems of HJB Equations
• Approximation of a degenerate semilinear PDEs with a nonlinear Neumann boundary condition
• Obstacle problem for SPDE with nonlinear Neumann boundary condition via reflected generalized backward doubly SDEs
• Obstacle problem for SPDE with nonlinear Neumann boundary condition via reflected generalized backward doubly SDEs
• Stochastic Homogenization of Reflected Diffusion Processes