Weak solutions to non-homogeneous boundary value problems for time-fractional diffusion equations

We discuss an initial-boundary problem for a time-fractional diffusion equation with non-zero Dirichlet boundary values which belong to L2 in time t and to a Sobolev space of negative order in space and prove the unique existence of weak solutions and a priori estimates. The proof is based on the Caputo fractional derivative in Sobolev spaces and the transposition method. We show one application to the existence of solution to an optimal control problem. © 2017 Elsevier Inc.

Авторы
Редакторы
-
Издательство
Academic Press Inc.
Номер выпуска
1
Язык
Английский
Страницы
365-381
Статус
Опубликовано
Подразделение
-
Номер
-
Том
460
Год
2018
Организации
  • 1 Department of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo 153, Japan
  • 2 Research Center of Nonlinear Problems of Mathematical Physics, Peoples' Friendship University of Russia, Moscow, Russian Federation
Ключевые слова
Non-homogeneous boundary value problem; Optimal control; Time-fractional diffusion equation; Weak solution
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6733/