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.

Authors
Publisher
Academic Press Inc.
Number of issue
1
Language
English
Pages
365-381
Status
Published
Volume
460
Year
2018
Organizations
  • 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
Keywords
Non-homogeneous boundary value problem; Optimal control; Time-fractional diffusion equation; Weak solution
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/6733/