Phragmén–Lindelöf Alternative Results for the Moore–Gibson–Thompson Heat Equation on an Exterior Region in R3

Jincheng Shi and Yiwu Lin

Journal of Mathematics, 2026, vol. 2026, 1-11

Abstract: This study presents investigates the spatial behavior of solutions to the Moore–Gibson–Thompson (MGT) heat conduction equation posed on an exterior domain in ℠3. Within the framework of Green–Naghdi Type III theory, we analyze the radial asymptotic properties of solutions using a novel weighted energy functional and a first-order differential inequality approach. It is rigorously established that the energy of the solution either exhibits exponential spatial growth or exponential decay as the radial distance r⟶∞–a sharp Phragmén–Lindelöf type alternative. This dichotomy constitutes a Saint–Venant-type principle for the MGT model in exterior geometries, explicitly characterizing its intrinsic spatial stability. Notably, the decay rate is shown to be adjustable via a free parameter, a feature distinctive to unbounded exterior settings. Our results contribute a systematic characterization of spatial asymptotics for the MGT equation in an exterior domain, a setting that has received less attention compared with the bounded or full-space cases for this equation.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9711660

DOI: 10.1155/jom/9711660

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