Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium

Abstract

AbstractThe paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem. This approach is consistent with the peculiarities of the problems — multiple solutions of the elliptic problem and blow-up solutions of the parabolic one.