Burning-Rate Coefficients in Solid Propellants: Modeling, Estimation, Stability and Numerical Illustration

Abstract

The burning-rate law is a central empirical and mathematical relation in the modelling of solid-propellant combustion. In its classical Saint Robert–Vieille form, it is written as r = aPⁿ, where r is the linear burning rate, P is pressure, a is the burning-rate coefficient and n is the pressure exponent. This revised manuscript develops a coherent mathematical framework for estimating a and n, quantifying uncertainty, and embedding the fitted coefficients into nonstationary pressure dynamics. The model is extended to include thermal memory through discrete-delay and distributed-memory functional differential equations. Existence, uniqueness, positivity, continuous dependence, local and global stability, delay thresholds and Lyapunov–Krasovskii stability are stated as formal results. Each theorem is accompanied by a numerical illustration with clear colour graphics, including pressure-response curves, stability surfaces, kernel effects and Lyapunov decay. The numerical section is written in a MATLAB/Python style so that the simulations can be reproduced without relying on propellant formulation or manufacturing details. The paper remains mathematical and modelling-oriented; it does not provide operational design instructions.