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Boundary layer solutions to singularly perturbed quasilinear systemsстатья
- Авторы: Butuzov V.F., Nefedov N.N., Omel'chenko O., Recke L.
- Журнал: Discrete and Continuous Dynamical Systems - Series B
- Том: 27
- Номер: 8
- Год издания: 2022
- Издательство: American Institute of Mathematical Sciences
- Местоположение издательства: United States
- Первая страница: 4255
- Последняя страница: 4283
- DOI: 10.3934/dcdsb.2021226
- Аннотация: Abstract. We consider weak boundary layer solutions to the singularly per-turbed ODE systems of the type ε2 (A(x, u(x), ε)ut(x))t = f (x, u(x), ε). The new features are that we do not consider one scalar equation, but systems, that the systems are allowed to be quasilinear, and that the systems are spatially non-smooth. Although the results about existence, asymptotic behavior, local uniqueness and stability of boundary layer solutions are similar to those known for semilinear, scalar and smooth problems, there are at least three essential differences. First, the asymptotic convergence rates valid for smooth problems are not true anymore, in general, in the non-smooth case. Second, a specific local uniqueness condition from the scalar case is not sufficient anymore in the vectorial case. And third, the monotonicity condition, which is sufficient for stability of boundary layers in the scalar case, must be adjusted to the vectorial case.
- Добавил в систему: Нефедов Николай Николаевич