Existence of Pulses for the System of Competition of Species
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The paper is concerned with the existence of pulses for monotone reaction–diffusion systems of two equations. For a general class of systems we prove that pulses exist if and only if the wave solutions propagate at positive speed. This result is applied to investigate the existence of pulses for the system of competition of species.
KeywordsExistence of pulses Monotone systems Leray–Schauder method
Mathematics Subject Classification35K57 47F05
The second author was partially supported by the Ministry of Education and Science of the Russian Federation (the Agreement Number 02.a03.21.0008) and by the program PICS CNRS 6583 Matbio.
- 7.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
- 8.Volpert, A.I., Volpert, V.A., Volpert, V.A.: Travelling wave solutions of parabolic systems. In: Translation of Mathematical Monographs, vol. 140. American Mathematical Society, Providence (1994)Google Scholar
- 10.Volpert, V., Volpert, A.: Properness and topological degree for general elliptic operators. Abstr. Appl. Anal. 2003(3), 129–181 (2003)Google Scholar
- 11.Volpert, V.: Elliptic partial differential equations, Volume 1, Fredholm theory of elliptic problems in unbounded domains. Birkhäuser, Basel (2011)Google Scholar
- 12.Volpert, V.: Elliptic partial differential equations, Volume 2, reaction–diffusion equations. Birkhäuser, Basel (2014)Google Scholar