Abstract
We consider a reaction–diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction–diffusion equations with unbounded time-dependent coefficients and different polynomial reaction terms. An exponential decay of the globally bounded solutions is proved. The key tool of the proofs are properties of analytic semigroups and some inequalities.
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Acknowledgements
The authors would like to express their gratitude to the Editors for handling the paper and to the anonymous referee for the attentive reading and insightful suggestions which improved the manuscript. We also express our deep thanks to Bao Quoc Tang for providing us with the proof of Theorem 1.1 and for interesting discussions. The second author is very grateful to the IRC for Intelligent Manufacturing and Robotics in King Fahd University of Petroleum and Minerals for its continuous support through Project No: SB201006.
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Majdoub, M., Tatar, NE. Global Existence and Asymptotic Behavior for a Reaction–Diffusion System with Unbounded Coefficients. Mediterr. J. Math. 20, 189 (2023). https://doi.org/10.1007/s00009-023-02394-2
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DOI: https://doi.org/10.1007/s00009-023-02394-2