Reconstruction of source function in a parabolic equation using partial boundary measurements

2025/04/22 by Tarun Sharma, Sharma, T., Larisa Beilina +3
Computer Science · Mathematics · #35K05 #35R30 #65J22 #65K10 #65M06 #65M32 #65M55 #65N21 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2504.16070

openalex publication_date 2025/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present the analytical and numerical study of the optimization approach for determining the space-dependent source function in the parabolic inverse source problem using partial boundary measurements. The Lagrangian approach for the solution of the optimization problem is presented, and optimality conditions are derived. The proof of the Fréchet differentiability of the regularized Tikhonov functional and the existence result for the solution of the inverse source problem are established. A local stability estimate for the unknown source term is also presented. The numerical examples justify the theoretical investigations using the conjugate gradient method (CGM) in 2D and 3D tests with noisy data.

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