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Structural stability and stabilization of solutions of the reversible three‐component Gray‐Scott system
Author(s) -
Kalantarova Jamila,
Uğurlu Davut
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5605
Subject(s) - mathematics , bounded function , autocatalysis , dirichlet distribution , neumann boundary condition , dirichlet boundary condition , mathematical analysis , component (thermodynamics) , domain (mathematical analysis) , reaction–diffusion system , stability (learning theory) , boundary (topology) , gray (unit) , boundary value problem , thermodynamics , kinetics , computer science , classical mechanics , physics , machine learning , medicine , radiology
This paper is concerned with the structural stability and stabilization of solutions to the three‐component reversible Gray‐Scott system under the Dirichlet or Neumann boundary conditions defined in a bounded domain of R n for 1 ≤ n ≤ 3. We prove that each solution depends on changes in a coefficient of the ratio of the reverse and forward reaction rates for the autocatalytic reaction as well as proving the continuous dependence on the initial data. We also prove that under Dirichlet's boundary conditions, the system is stabilized to the stationary solution by finitely many Fourier modes.