SPDEs with non-Lipschitz coefficients and nonhomogeneous boundary conditions

Xiong，Jie1; Yang，Xu2

2023-11-01

10.3150/22-BEJ1571

Bernoulli   Impact Factor & Quartile

1350-7265

In this article, we consider a stochastic partial differential equation (SPDE) driven by Gaussian colored noise with Dirichlet, Neumann or mixed nonhomogeneous random boundary conditions when the drift and diffusion coefficients are non-Lipschitz. We prove the existence of a unique strong solution to this SPDE and obtain a comparison theorem between such SPDEs. We also study the Hölder continuity of the solution in both time and space variables, and find the dependence of the Hölder exponent on that of the Dirichlet boundary.

Boundary conditions comparison theorem Hölder continuity non-Lipschitz coefficients pathwise uniqueness stochastic partial differential equation

English

First

National Natural Science Foundation of China[11831010];National Natural Science Foundation of China[12061004];National Natural Science Foundation of China[61873325];

MATHEMATICS

2-s2.0-85163979086

Scopus

1.Department of Mathematics and SUSTech International center for Mathematics,Southern University of Science and Technology,Shenzhen,China
2.School of Mathematics and Information Science,North Minzu University,Yinchuan,China

Xiong，Jie,Yang，Xu. SPDEs with non-Lipschitz coefficients and nonhomogeneous boundary conditions[J]. Bernoulli,2023,29(4):2987-3012.

Xiong，Jie,&Yang，Xu.(2023).SPDEs with non-Lipschitz coefficients and nonhomogeneous boundary conditions.Bernoulli,29(4),2987-3012.

Xiong，Jie,et al."SPDEs with non-Lipschitz coefficients and nonhomogeneous boundary conditions".Bernoulli 29.4(2023):2987-3012.