SPDEs with non-Lipschitz coefficients and nonhomogeous boundary conditions

TL;DR

This paper proves the existence, uniqueness, and comparison results for SPDEs with non-Lipschitz coefficients and nonhomogeneous boundary conditions, analyzing solution regularity in time and space.

Contribution

It establishes strong solutions and comparison theorems for SPDEs with non-Lipschitz drift and nonhomogeneous boundary conditions, extending existing theory.

Findings

Proved strong existence and pathwise uniqueness of solutions.

Established a comparison theorem for the SPDEs.

Analyzed H"older continuity of solutions in time and space.

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.