Existence of Waves for a Bistable Reaction–Diffusion System with Delay

Abstract

Existence of travelling waves is studied for a delay reaction–diffusion system of equations describing the distribution of viruses and immune cells in the tissue. The proof uses the Leray-Schauder method based on the topological degree for elliptic operators in unbounded domains and on a priori estimates of solutions in weighted spaces.

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Acknowledgements

The publication has been prepared with the support of the “RUDN University Program 5-100”, the Russian Science Foundation grant number 18-11-00171, and the French–Russian project PRC2307. The author is grateful to the anonymous reviewer for the profound reading of the paper and for the valuable remarks.

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Volpert, V. Existence of Waves for a Bistable Reaction–Diffusion System with Delay. J Dyn Diff Equat 32, 615–629 (2020). https://doi.org/10.1007/s10884-019-09751-4

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Keywords

  • Reaction–diffusion system
  • Delay
  • Travelling wave
  • Existence

Mathematics subject classification

  • 35K57