Asymptotic behaviour of solutions to one-dimensional reaction diffusion cooperative systems involving infinitesimal generators. (English) Zbl 1338.35486

Yangari, Miguel

J. Appl. Anal. 22, No. 1, 55-65 (2016).

Summary: 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.

MSC:

35R11	Fractional partial differential equations
35B40	Asymptotic behavior of solutions to PDEs
35B51	Comparison principles in context of PDEs

Keywords:

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

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