Diffusion in media with membranes and some nonlocal parabolic problems

Bohdan Kopytko; Mykhailo Osypchuk; Roman Shevchuk

doi:10.3842/umzh.v75i11.7379

Bohdan Kopytko Department of Mathematics, Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Poland
Mykhailo Osypchuk Department of Mathematical and Functional Analysis, Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
Roman Shevchuk Department of Mathematics, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, Ukraine

DOI: https://doi.org/10.3842/umzh.v75i11.7379

Ключові слова: параболічний потенціал, гранична умова Вентцеля, напівгрупа Феллера, метод послідовних наближень

Анотація

УДК 519.21

Дифузія в середовищах з мембранами та деякі нелокальні параболічні задачі

Встановлено класичну розв'язність однієї задачі спряження для одновимірного (за просторовою змінною) оберненого рівняння Колмогорова з розривними коефіцієнтами та заданими на негладких межах розглядуваних криволінійних областей деякими варіантами загальної нелокальної крайової умови типу Феллера–,Вентцеля. Крім того, доведено, що визначена за допомогою розв'язку цієї задачі двопараметрична напівгрупа Феллера описує на заданому проміжку числової прямої деякий неоднорідний дифузійний процес з рухомими мембранами. Показано також зв'язок побудованого процесу з узагальненою дифузією в розумінні М. І. Портенка.

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