On uniqueness of semi-wavefronts

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• 作者：Maitere Aguerrea (1) maguerrea@ucm.cl
  Carlos Gomez (2) cgomez@inst-mat.utalca.cl
  Sergei Trofimchuk (2) trofimch@inst-mat.utalca.cl
• 关键词：Mathematics Subject Classification (2010) 45J10 &#8211 ; 45J05 &#8211 ; 35K57 &#8211 ; 35C07
• 刊名：Mathematische Annalen
• 出版年：2012
• 出版时间：September 2012
• 年：2012
• 卷：354
• 期：1
• 页码：73-109
• 全文大小：400.9 KB
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• 作者单位：1. Facultad de Ciencias B谩sicas, Universidad Cat贸lica del Maule, Casilla 617, Talca, Chile2. Instituto de Matem谩tica y Fisica, Universidad de Talca, Casilla 747, Talca, Chile
• ISSN：1432-1807

文摘

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.