Structural Stability of the Moore–Gibson–Thompson Heat Equation in a Semi‐Infinite Cylindrical Domain

This work analyzes the continuous dependence of solutions to the Moore–Gibson–Thompson (MGT) equation formulated via Green–Naghdi Type III second gradient elasticity theory. The governing system is defined on a semi‐infinite cylindrical domain, subject to homogeneous Dirichlet conditions on the lateral boundary. Initial data are prescribed on the finite end, while appropriate asymptotic decay is assumed at infinity. By employing an integral–differential inequality technique, a stability estimate with respect to the coefficient k ∗ is established. The result demonstrates that the solution exhibits exponential decay along the axial coordinate z and converges uniformly to zero as the parameter k ∗ tends to zero.