Existence of Waves for a Bistable Reaction–Diffusion System with Delay
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.
KeywordsReaction–diffusion system Delay Travelling wave Existence
Mathematics subject classification35K57
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.
- 15.Trofimchuk, S., Volpert, V.: Global continuation of monotone waves for bistable delayed equations with unimodal nonlinearities. Nonlinearity (2019). in pressGoogle Scholar
- 16.Volpert, V.: Existence of viral infection waves in a model of immune response. In pressGoogle Scholar
- 17.Volpert, A.I., Volpert, V.A.: Applications of the rotation theory of vector fields to the study of wave solutions of parabolic equations. Trans. Moscow Math. Soc. 52, 59–108 (1990)Google Scholar
- 18.Volpert, A., Volpert, Vit., Volpert, Vl.: Traveling wave solutions of parabolic systems. Translation of mathematical monographs, Vol. 140, Amer. Math. Society, Providence (1994)Google Scholar