On a Robust Stability Criterion of the Radially Symmetric Heat Equation

This paper establishes a robust stability criterion in the radially symmetric heat equation that admits heat sources belonging to a set of bounded functions. The robust stability criterion is determined by extending a definition of stability under constant-acting perturbations that was originally established for systems of ordinary differential equations. It is assumed that heat sources admit a Fourier series representation whose coefficients are bounded and piecewise continuous functions. The robust stability criterion obtained is useful to conclude that the solution of the heat equation, as well as its first partial derivatives with respect to the radial axis and with respect to time, are bounded by a constant whose value is initially established. The results obtained are illustrated numerically.