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existence of waves

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Existence of bistable waves for a nonlocal and nonmonotone reaction-diffusion equation
Part of
- Functional-differential and differential-difference equations
- Parabolic equations and systems
Sergei Trofimchuk, Vitaly Volpert
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 2 / April 2020

Published online by Cambridge University Press:

23 January 2019, pp. 721-739

Print publication:

April 2020
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Reaction-diffusion equation with a bistable nonlocal nonlinearity is considered in the case where the reaction term is not quasi-monotone. For this equation, the existence of travelling waves is proved by the Leray-Schauder method based on the topological degree for elliptic operators in unbounded domains and a priori estimates of solutions in properly chosen weighted spaces.