Exact Solutions with Generalized Separation of Variables of the Nonlinear Heat Equation with a Source

Abstract

We propose a method for the construction of exact solutions to the nonlinear heat equation with a source based on the classical method of separation of variables, its generalization, and the method of reduction. We consider substitutions reducing the nonlinear heat equation to ordinary differential equations and to a system of two ordinary differential equations. The classes of exact solutions of the analyzed equation are constructed by the method of generalized separation of variables.