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

  • V. VolpertEmail author


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.


Reaction–diffusion system Delay Travelling wave Existence 

Mathematics subject classification




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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Authors and Affiliations

  1. 1.Institut Camille Jordan, UMR 5208 CNRSUniversity Lyon 1VilleurbanneFrance
  2. 2.Institut Camille JordanINRIA, Université de Lyon, Université Lyon 1Villeurbanne CedexFrance
  3. 3.Peoples Friendship University of Russia (RUDN University)MoscowRussian Federation
  4. 4.Marchuk Institute of Numerical Mathematics of the RAS ul. Gubkina 8MoscowRussian Federation

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