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 $A$.File | Dimensione | Formato | |
---|---|---|---|
Floridia_Equation_2020.pdf
solo gestori archivio
Note: Versione editoriale
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
145.52 kB
Formato
Adobe PDF
|
145.52 kB | Adobe PDF | Contatta l'autore |
2001.09444.pdf
accesso aperto
Note: Versione depositata su ArXiv
Tipologia:
Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
222.36 kB
Formato
Adobe PDF
|
222.36 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.