A Reconstruction Algorithm for a Semilinear Parabolic Inverse Problem

2014/12/22 by Wuqing Ning, Ning, Wuqing, Xue Qin +3
Computer Science · Mathematics · #35K55 #35R30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #math.AP #msc:35K55 #msc:35R30

paper · pdf · doi:10.48550/arxiv.1412.7114

7 pages, 16 references

arxiv created 2014/12/22 · openalex publication_date 2014/12/22 · arxiv updated 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider an inverse problem to determine a semilinear term of a parabolic equation from a single boundary measurement of Neumann type. For this problem, a reconstruction algorithm is established by the spectral representation for the fundamental solution of heat equation with homogeneous Neumann boundary condition and the Whitney extension theorem.

Related

• Recovery of nonlinear terms for reaction diffusion equations from boundary measurements
• Numerical methods for reconstruction of source term of heat equation from the final overdetermination
• Partial data inverse problems for reaction-diffusion and heat equations
• A new algorithm to determine the creation or depletion term of parabolic equations from boundary measurements
• A time-dependent inverse source problem for a semilinear pseudo-parabolic equation with Neumann boundary condition