Well-posedness for the backward problems in time for general time-fractional diffusion equation

In this article, we consider an evolution partial differential equation with Caputo time-derivative with the zero Dirichlet boundary condition: partial derivative(alpha)(t)u + Au - F where 0 < alpha < 1 and the principal part -A, is a non-symmetric elliptic operator of the second order. Given a source F. we prove the well-posedness for the backward problem in time and our result generalizes the existing results assuming that -A is symmetric. The key is a perturbation argument and the completeness of the generalized eigenfunctions of the elliptic operator A.

Authors
Floridia G.1 , Li Z.Y.2 , Yamamoto M. 3, 4, 5
Publisher
European Mathematical Society Publishing House
Number of issue
3
Language
English
Pages
593-610
Status
Published
Volume
31
Year
2020
Organizations
  • 1 Univ Mediterranea Reggio Calabria, Dept PAU, Via Univ 25, I-89124 Reggio Di Calabria, Italy
  • 2 Shandong Univ Technol, Sch Math & Stat, Zibo 255049, Shandong, Peoples R China
  • 3 Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan
  • 4 Acad Romanian Scientists, Splaiul Independentei St 54, Bucharest 050094, Romania
  • 5 Peoples Friendship Univ Russia RUDN Univ, 6 Miklukho Maklaya St, Moscow 117198, Russia
Keywords
Fractional PDE; backward problem; well-posedness
Date of creation
20.04.2021
Date of change
20.04.2021
Short link
https://repository.rudn.ru/en/records/article/record/73159/
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