SPDEs with non-Lipschitz coefficients and nonhomogeous boundary conditions

Jie Xiong; Xu Yang

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arXiv · 2006.01009

SPDEs with non-Lipschitz coefficients and nonhomogeous boundary conditions

Jie Xiong·Xu Yang

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Abstract

In this paper we establish the strong existence, pathwise uniqueness and a comparison theorem to a stochastic partial differential equation driven by Gaussian colored noise with non-Lipschitz drift, H\"older continuous diffusion coefficients and the spatial domain in finite interval, $[0,1]$, and with Dirichlet, Neumann or mixed nonhomogeneous random conditions imposed on the endpoints. The H\"older continuity of the solution both in time and in space variables is also studied.

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Jie Xiong, Xu Yang. 2020-06-01. SPDEs with non-Lipschitz coefficients and nonhomogeous boundary conditions. https://arxiv.org/abs/2006.01009

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