A Reconstruction Algorithm for a Semilinear Parabolic Inverse Problem
  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. 
Wuqing Ning, Xue Qin and Yunxia Shang
math.AP