Global Existence and Asymptotic Stability for a Class of Coupled Reaction-Diffusion Systems on Growing Domains

Abstract

The main purpose of this paper is to extend the result of Barabanova (Proc. Am. Math. Soc. 122:827–831, 1994) on the global existence, uniqueness, uniform boundedness, and the asymptotic behavior of solutions for a weakly coupled class of reaction-diffusion systems on a growing domain with an isotropic growth. Numerical simulations are used to affirm and support the analytical findings.

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Acknowledgements

We are grateful to the anonymous referees for their accurate revision of the manuscript and their valuable and constructive comments. The authors also would like to thank Professors Amar Youkana, Mokhtar Kirane and Zhigui Lin for their discussion from which we have benefited immensely. This work would not have been possible without the financial support of the Directorate-General for Scientific Research and Technological Development (DGRSDT) of Algeria.

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Correspondence to Salem Abdelmalek.

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Douaifia, R., Abdelmalek, S. & Bendoukha, S. Global Existence and Asymptotic Stability for a Class of Coupled Reaction-Diffusion Systems on Growing Domains. Acta Appl Math 171, 17 (2021). https://doi.org/10.1007/s10440-021-00385-7

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Keywords

  • Reaction-diffusion systems
  • Global existence
  • Evolving domain
  • Global asymptotic stability
  • Lyapunov function