In this article, we consider an evolution partial differential equation with Caputo time-derivative with the zero Dirichlet boundary condition: $pppa u + Au = F$ 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 $A$.

Well-posedness for the backward problems in time for general time-fractional diffusion equation / Floridia, Giuseppe; Li, Zhiyuan; Yamamoto, Masahiro. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 31:3(2020), pp. 593-610. [10.4171/RLM/906]

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

Floridia, Giuseppe;
2020

Abstract

In this article, we consider an evolution partial differential equation with Caputo time-derivative with the zero Dirichlet boundary condition: $pppa u + Au = F$ 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 $A$.
2020
Fractional PDE; backward problem; well-posedness
01 Pubblicazione su rivista::01a Articolo in rivista
Well-posedness for the backward problems in time for general time-fractional diffusion equation / Floridia, Giuseppe; Li, Zhiyuan; Yamamoto, Masahiro. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 31:3(2020), pp. 593-610. [10.4171/RLM/906]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654743
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