Towards the Differences in Behaviour of Solutions of Linear and Non-linear Heat-conduction Equations

Abstract

The linear and non-linear heat-conduction equations are analyzed by the previously initiated geometrical method of analyzing linear and non-linear equations in partial derivatives. The reason of the difference in behavior of solutions of equations under consideration was stated, as well as the reason of aggravation of the non-linear equation. A class of solutions of linear equations that represents the surfaces of the levels of non-linear heat-conduction equations was excluded.