Neumann Boundary Problem for Parabolic Partial Differential Equations with Divergence Terms

Xue Yang; Jing Zhang

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arXiv · 1802.07626

Neumann Boundary Problem for Parabolic Partial Differential Equations with Divergence Terms

Xue Yang·Jing Zhang

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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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Xue Yang, Jing Zhang. 2018-02-21. Neumann Boundary Problem for Parabolic Partial Differential Equations with Divergence Terms. https://arxiv.org/abs/1802.07626

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