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Existence of Contrast Structures in a Problem with Discontinuous Reaction and Advectionстатья
Статья опубликована в журнале из списка RSCI Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Nefedov N.N., Nikulin E.I., Orlov A.O.
- Журнал: Russian Journal of Mathematical Physics
- Том: 29
- Номер: 2
- Год издания: 2022
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 214
- Последняя страница: 224
- DOI: 10.1134/s1061920822020042
- Аннотация: In the paper, a boundary value problem for a singularly perturbed reaction-diffusion-advection equation is considered in a two-dimensional domain in the case of discontinuous coefficients of reaction and advection, whose discontinuity occurs on a predetermined curve lying in the domain. It is shown that this problem has a solution with a sharp internal transition layer localized near the discontinuity curve. For this solution, an asymptotic expansion in a small parameter is constructed, and also sufficient conditions are obtained for the input data of the problem under which the solution exists. The proof of the existence theorem is based on the asymptotic method of differential inequalities. It is also shown that a solution of this kind is Lyapunov asymptotically stable and locally unique. The results of the paper can be used to create mathematical models of physical phenomena at the interface between two media with different characteristics, as well as for the development of numerical-analytical methods for solving singularly perturbed problems.
- Добавил в систему: Орлов Андрей Олегович