Research on nuclear explosion inverse problem based on polar coordinate system

This study investigates two inverse problems for reconstructing the central temperature and blast radius of nuclear explosions using far-field temperature observation data in polar coordinates. The model exhibits singularity at [Formula: see text], significantly increasing the difficulty of theoretical analysis and numerical computation. First, based on the analytical solution of the forward problem, the inverse source problem is transformed into a first-kind Volterra integral equation, and the uniqueness of its solution are rigorously proved. Second, through nonlinear integral equation modeling in polar coordinates, the existence and uniqueness of the solution for the inverse blast radius problem are derived. For these two inverse problems, an iterative optimization algorithm based on Tikhonov regularization and a hybrid algorithm combining golden section search with gradient descent are proposed, respectively. Numerical experiments demonstrate the effectiveness of both methods in addressing ill-posedness and nonlinearity, successfully achieving high-precision reconstruction of the central temperature distribution and blast radius.