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Weak solutions of impulsive pseudoparabolic equations with an infinitesimal transition layer Научная публикация

Журнал Nonlinear Analysis
ISSN: 0362-546X
Вых. Данные Год: 2023, Том: 228, Номер статьи : 113190, Страниц : 20 DOI: 10.1016/j.na.2022.113190
Ключевые слова Pseudoparabolic equations, Impulsive equations, Weak solutions, Transition layer
Авторы Kuznetsov Ivan 1,2 , Sazhenkov Sergey 1,2
Организации
1 Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences
2 Altai State University, Laboratory for Mathematical and Computer Modeling in Natural and Industrial Systems

Информация о финансировании (1)

1 Министерство науки и высшего образования Российской Федерации FWGG-2021-0010

Реферат: We study the multi-dimensional initial-boundary value problem for the quasilinear pseudoparabolic equation with a regular nonlinear minor term, which models a non-instantaneous impulsive impact. The minor term depends on a small parameter $\varepsilon>0$ and, as $\varepsilon\to 0$, converges weakly$^\star$ to the expression incorporating the Dirac delta function, which, in turn, models an instantaneous impulsive impact. We prove that the infinitesimal transition layer, associated with the Dirac delta function, is formed as $\varepsilon\to 0$, and that the family of weak solutions of the original problem converges to the weak solution of a two-scale microscopic-macroscopic model. This model consists of two equations and the set of initial, boundary, and matching conditions, so that the `outer' macroscopic solution beyond the transition layer is governed by the quasilinear homogeneous pseudoparabolic equation at the macroscopic (`slow') timescale, while the transition layer solution is defined at the microscopic level and obeys the semilinear pseudoparabolic equation at the microscopic (`fast') timescale. The latter equation inherits the full information about the profile of the original non-instantaneous impulsive impact.
Библиографическая ссылка: Kuznetsov I. , Sazhenkov S.
Weak solutions of impulsive pseudoparabolic equations with an infinitesimal transition layer
Nonlinear Analysis. 2023. V.228. 113190 :1-20. DOI: 10.1016/j.na.2022.113190 WOS Scopus РИНЦ OpenAlex
Даты:
Поступила в редакцию: 2 авг. 2022 г.
Принята к публикации: 27 нояб. 2022 г.
Опубликована online: 12 дек. 2022 г.
Идентификаторы БД:
Web of science: WOS:000901766400002
Scopus: 2-s2.0-85143737224
РИНЦ: 54626731
OpenAlex: W4311421100
Цитирование в БД:
БД Цитирований
Scopus 4
OpenAlex 4
РИНЦ 3
Web of science 4
Альметрики: