Stability for inverse random source problems of the polyharmonic wave equation

Abstract

This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives stability estimates for identifying the strength of the random source. Assuming a priori information of the regularity and support of the source strength, the H\"{o}lder stability is established in the absence of a potential. In the more challenging case where a potential is present, the logarithmic stability estimate is obtained by constructing specialized solutions to the polyharmonic wave equation.