Existence and Stability of the Solution to a System of Two Nonlinear Diffusion Equations in a Medium with Discontinuous Characteristicsстатья
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: 26 января 2022 г.
Аннотация:Asymptotic analysis is used to study the existence, local uniqueness, and asymptotic Lyapunov stability of the solution to a one-dimensional nonlinear parabolic system of the activator–inhibitor type. A specific feature of the problem is the discontinuities of the first kind of the functionson the right-hand sides of the equations. The jump of the functions occurs at a single point of the interval on which the problem is considered. The solution with a large gradient in the vicinity of the discontinuity is studied. The existence and stability theorems are proved using the asymptotic method ofdifferential inequalities