The article considers self-similar solutions of the nonlinear heat equation with a three-dimensional source that evolve in a blow-up setting. The self-similar problem is a boundary-value problem for a nonlinear equation of elliptical type that has a nonunique solution. We investigate the eigenfunction spectrum of the self-similar problem in two- and three-dimensional space. The problem is solved on a grid by Newton’s iteration method. The implementation of Newton’s method requires analysis of a linearized equation and construction of initial approximations. The eigenfunctions are continued in a parameter. Structures of various symmetry are obtained. New types of multidimensional structures are observed: these are multiply connected three-dimensional heat localization regions.
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