At the previous conference, the authors made a presentation about a very effective way of destroying materials (including rocks) with the help of low-pressure chemically active jet (CJA) impact on them. Further study of the phenomenon led to the formulation of a mathematical problem about the penetration of the CAB in the destructible material. The formulation of this problem was accompanied by consideration of the spherically symmetric thermal conductivity equation with a boundary condition of the first kind and with a threshold criterion for thermal destruction.