On exact solutions to a heat wave propagation boundary-value problem for a nonlinear heat equation
А. Л. Казаков · Sibirskie Elektronnye Matematicheskie Izvestiya · 2019
The paper deals with a nonlinear second order parabolic PDE, which is usually called "the nonlinear heat equation".We construct and study a particular class of solutions having the form of a heat wave that propagates on a cold (zero) background with finite velocity.The equation degenerates on the front of a heat wave and its order decreases.This fact complicates the study.We prove a new existence and uniqueness theorem for a boundary-value problem with a given heat-wave front in the class of analytical functions.Also, we are looking for exact heatwave type solutions.The construction of these solutions is reduced to integration of the nonlinear second order ODE with singularity.