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

  • Giuseppe Floridia

    Università Mediterranea di Reggio Calabria, Italy
  • Zhiyuan Li

    Shandong University of Technology, Zibo, Shandong, China
  • Masahiro Yamamoto

    University of Tokyo, Japan
Well-posedness for the backward problems in time for general time-fractional diffusion equation cover

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Abstract

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

Cite this article

Giuseppe Floridia, Zhiyuan Li, Masahiro Yamamoto, Well-posedness for the backward problems in time for general time-fractional diffusion equation. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 3, pp. 593–610

DOI 10.4171/RLM/906