Open AccessRobust stability of the global attractor of the reaction-diffusion system
Author(s) -
O. V. Kapustyan,
AUTHOR_ID,
O. B. Kurylko,
T. V. Yusypiv,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2021
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2021/3.6
Subject(s) - attractor , decoupling (probability) , nonlinear system , mathematics , reaction–diffusion system , operator (biology) , trajectory , stability (learning theory) , control theory (sociology) , mathematical analysis , computer science , physics , biochemistry , chemistry , control (management) , repressor , quantum mechanics , control engineering , astronomy , machine learning , artificial intelligence , transcription factor , engineering , gene
In this paper we consider the problem of robust stability for a nonlinear system of equations in partial derivatives of the reaction-diffusion type. An undisturbed system is considered to have a global attractor. The main task is to estimate the deviation of the trajectory of the perturbed system from the global attractor of the perturbed system depending on the magnitude of the perturbations. Such an estimate can be obtained in the framework of the theory of input-to-state stability (ISS). The paper does not impose any conditions on the derivative of the nonlinear interaction function, so the unity of the solution of the initial problem is not ensured. The paper proposes a new approach to obtaining estimates of robust stability of the attractor in the case of a multivalued evolutionary decoupling operator. In particular, it is proved that the multivalued decoupling operator generated by weak solutions of a nonlinear reaction-diffusion system has the property of asymptotic gain (AG) with respect to the attractor of the undisturbed system.