Robust stability of the global attractor of the reaction-diffusion system

Тип публікації :
Стаття
Дата випуску :
2021
Автор(и) :
Капустян, О. В.
Курилко, О. Б.
Юсипів, Т. В.
Мова основного тексту :
Англійська
eKNUTSHIR URL :
DOI :
Журнал :
Випуск :
3
ISSN :
1812-5409
Початкова сторінка :
46
Кінцева сторінка :
50
Цитування :
[APA 7] Капустян, О. В., Курилко, О. Б., & Юсипів, Т. В. (2021). Robust stability of the global attractor of the reaction-diffusion system. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (3), 46–50. https://doi.org/10.17721/1812-5409.2021/3.6
[ДСТУ] Капустян О. В., Курилко О. Б., Юсипів Т. В. Robust stability of the global attractor of the reaction-diffusion system. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics. 2021. no. 3. P. 46—50. DOI: 10.17721/1812-5409.2021/3.6 (date of access: 25.07.2026).
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.
Pages of the article in the issue: 46 - 50
Language of the article: Ukrainian
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