Self-similar solutions to the Cauchy problem for a nonlinear heat equation (Q1571161)

All possible power-scaling self-similar solutions to the Cauchy problem for a one-dimensional nonlinear heat equation with power nonlinearity are analyzed on the time interval \(0<t<+\infty\) in Cartesian, cylindrical, and spherical coordinates. The existence conditions and the properties of the solutions are determined as depending on the parameters of the problem. A number of new heating and cooling modes are found.