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Fechner, Włodzimierz

Journal of Applied Analysis

Editor-in-Chief: Liczberski, Piotr / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw

CiteScore 2017: 0.33

SCImago Journal Rank (SJR) 2017: 0.183
Source Normalized Impact per Paper (SNIP) 2017: 0.364

Mathematical Citation Quotient (MCQ) 2017: 0.27

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Volume 22, Issue 1


Asymptotic behaviour of solutions to one-dimensional reaction diffusion cooperative systems involving infinitesimal generators

Miguel Yangari
  • Corresponding author
  • Research Center on Mathematical Modelling (MODEMAT) and Department of Mathematics, Escuela Politécnica Nacional, Ladrón de Guevara E11-253, Quito, Ecuador
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Published Online: 2016-05-05 | DOI: https://doi.org/10.1515/jaa-2016-0006


The aim of this paper is to study the large-time behaviour of mild solutions to the one-dimensional cooperative systems with anomalous diffusion when at least one entry of the initial condition decays slower than a power. We prove that the solution moves at least exponentially fast as time goes to infinity. Moreover, the exponent of propagation depends on the decay of the initial condition and of the reaction term.

Keywords: Fractional Laplacian; reaction-diffusion systems; cooperative systems; time asymptotic propagation; exponential propagation

MSC: 35R11; 35B40; 35B51


  • 1

    D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math. 30 (1978), 33–76. Google Scholar

  • 2

    X. Cabre and J. Roquejoffre, The influence of fractional diffusion in Fisher–KPP equation, Comm. Math. Phys. 320 (2013), 679–722. Google Scholar

  • 3

    A.-C. Coulon and M. Yangari, Exponential propagation for fractional reaction-diffusion cooperative systems with fast decaying initial conditions, J. Dynam. Differential Equations (2015), 10.1007/s10884-015-9479-1. Google Scholar

  • 4

    P. Felmer and M. Yangari, Fast propagation for fractional KPP equations with slowly decaying initial conditions, SIAM J. Math. Anal. 45 (2013), 2, 662–678. Web of ScienceGoogle Scholar

  • 5

    F. Hamel and L. Roques, Fast propagation for KPP equations with slowly decaying initial conditions, J. Differential Equations 249 (2010), 1726–1745. Google Scholar

  • 6

    A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, Étude de l'equation de la diffusion avec croissance de la quantité de matiére et son application á un probléme biologique, Bull. Univ. État Moscou Sér. Inter. A 1 (1937), 1–26. Google Scholar

  • 7

    M. Lewis, B. Li and H. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol. 45 (2002), 219–233. Google Scholar

  • 8

    R. Lui, Biological growth and spread modeled by systems of recursions. I. Mathematical theory, Math. Biosci. 93 (1989), 2, 269–295. Google Scholar

  • 9

    H. F. Weinberger, M. Lewis and B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol. 45 (2002), 183–218. Google Scholar

  • 10

    H. F. Weinberger, M. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol. 55 (2007), 207–222. Web of ScienceGoogle Scholar

  • 11

    M. Yangari, Existence and uniqueness of global mild solutions for nonlocal Cauchy systems in Banach spaces, Rev. Politécnica 35 (2015), 2, 149–152. Google Scholar

About the article

Received: 2015-03-30

Revised: 2015-10-26

Accepted: 2015-11-12

Published Online: 2016-05-05

Published in Print: 2016-06-01

Citation Information: Journal of Applied Analysis, Volume 22, Issue 1, Pages 55–65, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: https://doi.org/10.1515/jaa-2016-0006.

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