On a robust stability criterion in the Cattaneo–Hristov diffusion equation

Abstract

The aim of this paper is to establish a robust stability criterion in the Cattaneo– Hristov diffusion equation moving over an interval under the influence of heat sources. The robust stability criterion arises as a generalization of the definition of stability under constant-acting perturbations that is employed in systems of differential equations. The criterion obtained allows to ensure that the solution of the Cattaneo–Hristov diffusion equation and its first partial derivatives with respect to the longitudinal axis and with respect to time can be bounded by a constant whose value is defined a priori. The criterion is illustrated by a numerical example.