Convergence to steady state solutions of a particular class of fracctional cooperative systems


  • Miguel Yangari Facultad de Ciencias Escuela Politécnica Nacional


The aim of this paper is to prove that under some appropriate assumptions on the nonlinearity and the initial datum, the solution of the fractional reaction-diffusion cooperative system converge to the smallest positive steady solution. Also, we prove that this convergence is exponential in time and that the exponent of propagation depends on the principal eigenvalue of the derivative of reaction term and on the smallest index of the fractional laplacians.


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Biografía del autor/a

Miguel Yangari, Facultad de Ciencias Escuela Politécnica Nacional

Profesor Titular Auxiliar.

Departamento de Matemática 


D.G. Aronson and H.F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math. 30, 1978, pp. 33-76.

H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. I. Species persistence, J. Math. Biol 51, 2005, pp. 75-113.

H. Berestycki, J.-M. Roquejoffre, and L. Rossi, The periodic patch model for population dynamics with fractional diffusion, Discrete Contin. Dyn. Syst. Ser. S 4, 2011, pp. 1-13.

X. Cabré and J. Roquejoffre. Propagation de fronts dans les équations de Fisher KPP avec diffusion fractionnaire. C. R. Math. Acad. Sci. Paris 347, 2009, pp. 1361-1366.

X. Cabré and J. Roquejoffre. The influence of fractional diffusion in Fisher-KPP equation. Commun. Math. Phys 320, 2013, pp 679-722.

A-C. Coulon and M. Yangari. (2014, Sept.), Exponential propagation for fractional reaction-diffusion cooperative systems with fast decaying

initial conditions, 2014, Available:


D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, New York, 1981, pp. 49-62.

A.N. Kolmogorov, I.G. Petrovsky and N.S. Piskunov, 'Etude de l'equation de la diffusion avec croissance de la quantit'e de mati'ere et son application 'a un probl'eme biologique, Bull. Univ. 'Etat Moscou S'er. Inter. A 1, 1937, pp. 1-26.

B. Li, H. Weinberger and M. Lewis. Spreading speeds as slowest wave speeds for cooperative systems. Math. Biosci. 196, 2005, pp. 82-98.

R. Mancinelli, D. Vergni, and A. Vulpiani. Front propagation in reactive systems with anomalous diffusion, Phys. D 185, 2003, pp. 175-195.

H.F. Weinberger, M. Lewis and B. Li. Analysis of linear determinacy for spread in cooperative models. J. Math. Biol. 45, 2002, pp. 183-218.




Cómo citar

Yangari, M. (2015). Convergence to steady state solutions of a particular class of fracctional cooperative systems. Revista Politécnica, 35(2), 12. Recuperado a partir de