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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.21756 |
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| _version_ | 1866913057980022784 |
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| author | Bomisso, Gossrin Jean-Marc Kouma, Ali Ouattara Anassé, Marie Esther |
| author_facet | Bomisso, Gossrin Jean-Marc Kouma, Ali Ouattara Anassé, Marie Esther |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21756 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximum principle and local stability for a class of coupled nonlinear thermo--reaction--phase systems Bomisso, Gossrin Jean-Marc Kouma, Ali Ouattara Anassé, Marie Esther Analysis of PDEs 35K57, 35B50, 35B35, 80A32 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. |
| title | Maximum principle and local stability for a class of coupled nonlinear thermo--reaction--phase systems |
| topic | Analysis of PDEs 35K57, 35B50, 35B35, 80A32 |
| url | https://arxiv.org/abs/2604.21756 |