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arXiv · 2604.21756

Maximum principle and local stability for a class of coupled nonlinear thermo--reaction--phase systems

Gossrin Jean-Marc Bomisso·Ali Ouattara Kouma·Marie Esther Anassé
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Abstract

We study a nonlinear coupled system of partial differential equations arising from thermo--reaction--phase models. The system combines a heat diffusion equation, temperature-dependent chemical reactions of Arrhenius type, and a phase variable, and is formulated as a strongly coupled parabolic problem with homogeneous Neumann boundary conditions. We first establish a maximum principle ensuring the positivity of the temperature on a suitable time interval, as well as the invariance of the physically admissible domain. In particular, we prove that the internal variables remain in the interval [0,1]. We then analyse the asymptotic behaviour of the system in the free regime, that is, in the absence of external forcing. By introducing a relative energy functional and exploiting the structure of the coupling terms, we obtain local asymptotic stability of a homogeneous stationary state. The model belongs to a broader class of coupled diffusion--reaction--phase systems.

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Gossrin Jean-Marc Bomisso, Ali Ouattara Kouma, Marie Esther Anassé. 2026-04-23. Maximum principle and local stability for a class of coupled nonlinear thermo--reaction--phase systems. https://arxiv.org/abs/2604.21756

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