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Analysis of the Weak Formulation of a Coupled Nonlinear Parabolic System Modeling a Heat Exchanger

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  • Kouma Ali Ouattara
  • Bomisso Gossrin Jean-Marc
  • Bérenger Akon Kpata
  • Touré Kidjégbo Augustin

Abstract

This paper establishes the existence, uniqueness and time–space regularity of the weak solution to a nonlinear coupled parabolic system modeling temperature evolution in a coaxial heat exchanger with source terms and spatially varying coefficients. The system is formulated in a weak sense and the analysis relies on a Faedo–Galerkin method tailored to handle the nonlinear coupling and heterogeneous domains. Under suitable assumptions on the initial data and source terms, enhanced regularity in both, time and space is obtained. In contrast with classical scalar models, the study addresses a multicomponent system with realistic boundary conditions and complex interfacial dynamics.MSC2020 Classification: 35K05, 35K55, 35A15, 35A01, 35A02, and 35A09

Suggested Citation

  • Kouma Ali Ouattara & Bomisso Gossrin Jean-Marc & Bérenger Akon Kpata & Touré Kidjégbo Augustin, 2025. "Analysis of the Weak Formulation of a Coupled Nonlinear Parabolic System Modeling a Heat Exchanger," Abstract and Applied Analysis, Hindawi, vol. 2025, pages 1-10, August.
    • Handle: RePEc:hin:jnlaaa:9186981
    DOI: 10.1155/aaa/9186981
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