Nonlinear Parabolic Inverse Problems-reconstruction Algorithm And Blow-up Inverse Problem

In this paper, we consider an inverse problem of a semilinear parabolic e-quation as follows: using the Dirichlet and Neumann boundary conditions to determine the unknown semilinear source function f, where the solution u is still unknown. According to the problem, we apply the spectral representation for the fundamental solution of heat equation with homogeneous Neumann bound-ary condition and the Whitney extension theorem to establish the theoretical reconstruction of f. Moreover, the iteration scheme of numerical reconstruction is obtained and the convergence theorem is proved. Eventually, we discuss the existence of a parabolic blow-up inverse problem.