Neumann Boundary Problem for Parabolic Partial Differential Equations with Divergence Terms
Probability
2018-02-22 v1
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.
Keywords
Cite
@article{arxiv.1802.07626,
title = {Neumann Boundary Problem for Parabolic Partial Differential Equations with Divergence Terms},
author = {Xue Yang and Jing Zhang},
journal= {arXiv preprint arXiv:1802.07626},
year = {2018}
}