On one class of exact solutions of the multidimensional nonlinear heat equation with a zero front

We consider a class of exact solutions of a multidimensional nonlinear heat equation with a source. The construction of these solutions leads to the solution of a family of second-order ordinary differential equations. If appropriate Cauchy conditions are specified, exact solutions can be interpreted as nontrivial solutions with zero front. An existence theorem is proved and a solution is constructed in the form of a converging power series. An approximate algorithm based on the collocation method of radial basis functions is proposed. Test calculations and numerical analysis of the solutions obtained are performed.