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The steady states of strong-KPP reactions in general domains

  • Henri Berestycki

    University of Maryland, College Park, USA; EHESS-CNRS, Paris, France; Hong Kong University of Science and Technology, Hong Kong

  • Cole Graham

    University of Wisconsin–Madison, Madison, USA
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Abstract

We study the uniqueness of steady states of strong-KPP reaction-diffusion equations in general domains under various boundary conditions. We show that positive bounded steady states are unique provided the domain satisfies a certain spectral nondegeneracy condition. We also formulate a number of open problems and conjectures.

Cite this article

Henri Berestycki, Cole Graham, The steady states of strong-KPP reactions in general domains. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1578