Neumann Boundary Problem for Parabolic Partial Differential Equations with Divergence Terms

2018/02/21 by Yang, Xue, Zhang, Jing
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1802.07626

Abstract

We prove an existence and uniqueness result for Neumann boundary problem of a parabolic partial differential equation (PDE for short) with a singular nonlinear divergence term which can only be understood in a weak sense. A probabilistic approach is applied by studying the backward stochastic differential equations (BSDEs for short) corresponding to the PDEs, the solution of which turns out to be a limit of a sequence of BSDEs constructed by penalization method.

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