2025/05/12 by Zhanna D. Totieva, Totieva, Zhanna D., Kush Kinra +3
Engineering · Mathematics · #35L05 #35L20 #35Q99 #35R30 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations
paper · doi:10.48550/arxiv.2505.07405
openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A wave equation with initial and acoustic boundary conditions in media with dispersion is used as a mathematical model. The inverse problem is reduced to an equivalent problem with homogeneous boundary conditions for the system of integro-differential equations. Using the technique of estimating integral equations and the contraction mappings principle in Sobolev spaces, the global existence and uniqueness theorem for the inverse problem is proved.