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On uniqueness of semi-wavefronts

Diekmann–Kaper theory of a nonlinear convolution equation re-visited

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Abstract

Motivated by the uniqueness problem for monostable semi-wave-fronts, we propose a revised version of the Diekmann and Kaper theory of a nonlinear convolution equation. Our version of the Diekmann–Kaper theory allows (1) to consider new types of models which include nonlocal KPP type equations (with either symmetric or anisotropic dispersal), nonlocal lattice equations and delayed reaction–diffusion equations; (2) to incorporate the critical case (which corresponds to the slowest wavefronts) into the consideration; (3) to weaken or to remove various restrictions on kernels and nonlinearities. The results are compared with those of Schumacher (J Reine Angew Math 316: 54–70, 1980), Carr and Chmaj (Proc Am Math Soc 132: 2433–2439, 2004), and other more recent studies.

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Authors and Affiliations

  1. Facultad de Ciencias Básicas, Universidad Católica del Maule, Casilla 617, Talca, Chile

    Maitere Aguerrea

  2. Instituto de Matemática y Fisica, Universidad de Talca, Casilla 747, Talca, Chile

    Carlos Gomez & Sergei Trofimchuk

Authors
  1. Maitere Aguerrea
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  2. Carlos Gomez
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  3. Sergei Trofimchuk
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Correspondence to Sergei Trofimchuk.

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Aguerrea, M., Gomez, C. & Trofimchuk, S. On uniqueness of semi-wavefronts. Math. Ann. 354, 73–109 (2012). https://doi.org/10.1007/s00208-011-0722-8

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  • DOI: https://doi.org/10.1007/s00208-011-0722-8

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