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

• Autorzy: Yangari M.

Identyfikatory

DOI

10.1515/jaa-2016-0006

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

fractional Laplacian; reaction-diffusion systems; cooperative systems; time asymptotic propagation; exponential propagation

PL

laplasjan ułamkowy; układy reakcji-dyfuzji; układ kooperacyjny; propagacja

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2016
• Tom: Vol. 22, nr 1
• Strony: 55--65
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Yangari M.

• Research Center on Mathematical Modelling (MODEMAT) and Department of Mathematics, Escuela Politécnica Nacional, Ladrón de Guevara E11-253, Quito, Ecuador

Bibliografia

• [1] D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math. 30 (1978), 33-76.
• [2] X. Cabre and J. Roquejoffre, The influence of fractional diffusion in Fisher-KPP equation, Comm. Math. Phys. 320 (2013), 679-722.
• [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), DOI 10.1007/s10884-015-9479-1.
• [4] P. Felmer and M. Yangari, Fast propagation for fractional KPP equations with slowly decaying initial conditions, SIAM J. Math. Anal. 45 (2013), no. 2, 662-678.
• [5] F. Hamel and L. Roques, Fast propagation for KPP equations with slowly decaying initial conditions, J. Differential Equations 249 (2010), 1726-1745.
• [6] A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, Etude de l'équation de la diffusion avec croissance de la quantité de matière et son application a un problème biologique, Bull. Univ. État Moscou Sér. Inter. A1 (1937), 1-26.
• [7] M. Lewis, B. Li and H. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Bbl 45(2002), 219-233.
• [8] R. Lui, Biological growth and spread modeled by systems of recursions. I. Mathematical theory, Math. Biosci. 93 (1989), no. 2, 269-295.
• [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.
• [10] H. F. Weinberger, M. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems, j. Math. Biol. 55 (2007), 207-222.
• [11] M. Yangari, Existence and uniqueness of global mild solutions for nonlocal Cauchy systems in Banach spaces, Rev. Politécnica 35 (2015), no. 2,149-152.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.