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Development of Methods of Asymptotic Analysis of TransitionLayers in Reaction–Diffusion–Advection Equations:Theory and Applicationsстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 4 марта 2022 г.
- Автор: Nefedov N.N.
- Журнал: Computational Mathematics and Mathematical Physics
- Том: 61
- Номер: 12
- Год издания: 2021
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 2068
- Последняя страница: 2087
- DOI: 10.1134/S0965542521120095
- Аннотация: This work presents a review and analysis of modern asymptotic methods for analysis of sin-—gularly perturbed problems with interior and boundary layers. The central part of the work is a reviewof the work of the author and his colleagues and disciples. It highlights boundary and initial-boundaryvalue problems for nonlinear elliptic and parabolic partial differential equations, as well as periodicparabolic problems, which are widely used in applications and are called reaction–diffusion and reac-tion–diffusion–advection equations. These problems can be interpreted as models in chemical kinet-ics, synergetics, astrophysics, biology, and other fields. The solutions of these problems often haveboth narrow boundary regions of rapid change and inner layers of various types (contrasting struc-tures, moving interior layers: fronts), which leads to the need to develop new asymptotic methods inorder to study them both formally and rigorously. A general scheme for a rigorous study of contraststructures in singularly perturbed problems for partial differential equations, based on the use of theasymptotic method of differential inequalities, is presented and illustrated on relevant problems. Themain achievements of this line of studies of partial differential equations are ref lected, and the keydirections of its development are indicated.
- Добавил в систему: Нефедов Николай Николаевич