SPDEs with non-Lipschitz coefficients and nonhomogeous boundary conditions

2020/06/01 by Xiong, Jie, Yang, Xu
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2006.01009

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, Hölder 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 Hölder continuity of the solution both in time and in space variables is also studied.

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