Calculus of Variations and Geometric Measure Theory
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G. Floridia - M. Yamamoto

Backward problems in time for fractional diffusion-wave equation

created by floridia on 21 Jul 2020

[BibTeX]

preprint

Inserted: 21 jul 2020

Year: 2020

ArXiv: 2007.09364 PDF

Abstract:

In this article, for a time-fractional diffusion-wave equation $\pppa u(x,t) = -Au(x,t)$, $0<t<T$ with fractional order $\alpha \in (1,2)$, we consider the backward problem in time: determine $u(\cdot,t)$, $0<t<T$ by $u(\cdot,T)$ and $\ppp_tu(\cdot,T)$. We proved that there exists a countably infinite set $\Lambda \in (0,\infty)$ with a unique accumulation point $0$ such that the backward problem is well-posed for $T \not\in \Lambda$.

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