Existence of bistable waves for a nonlocal and nonmonotone reaction-diffusion equation

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. © Royal Society of Edinburgh 2019.

Authors
Trofimchuk S. 1 , Volpert V. 2, 3, 4, 5
Journal
Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Publisher
Cambridge University Press
Language
English
State
Published
Link
External link
DOI
10.1017/PRM.2018.164
Year
2019
Organizations
  • 1 Instituto de Matemática y Fisica, Universidad de Talca, Talca, Chile
  • 2 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, 69622, France
  • 3 INRIA, Université de Lyon, Université Lyon 1, Institut Camille Jordan, du 11 Novembre 1918, Villeurbanne, Cedex, 69200, France
  • 4 People's Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
  • 5 Marchuk Institute of Numerical Mathematics, RAS, ul. Gubkina 8, Moscow, 119333, Russian Federation
Keywords
bistable nonlinearity; existence of waves; Leray-Schauder method; nonlinear Fredholm operator; nonlocal; Reaction-diffusion equation
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