2025/03/24 by Blåsten, Emilia L. K., Helin, Tapio, Kujanpää, Antti +2 · 1 citation
#35R30 #60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2503.18515
We consider the following inverse problem: Suppose a (1+1)-dimensional wave equation on ℝ+ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data at the same point, determine the unknown first order coefficient function of the system. We first establish that direct problem is well-posed. The inverse problem is then solved by showing that correlations of the boundary data determine the Neumann-to-Dirichlet operator in the sense of distributions, which is known to uniquely identify the coefficient. This approach has applications in acoustic measurements of internal cross-sections of fluid pipes such as pressurised water supply pipes and vocal tract shape determination.