Volume 29, 2023
|Number of page(s)||22|
|Published online||01 August 2023|
Analyticity and observability for fractional order parabolic equations in the whole space
School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, PR China.
2 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China.
* Corresponding author: email@example.com
Accepted: 6 July 2023
In this paper, we study the quantitative analyticity and observability inequality for solutions of fractional order parabolic equations with space-time dependent potentials in ℝn. We first obtain a uniformly lower bound of analyticity radius of the spatial variable for the above solutions with respect to the time variable. Next, we prove a globally Hölder-type interpolation inequality on a thick set, which is based on a propagation estimate of smallness for analytic functions. Finally, we establish an observability inequality from a thick set in ℝn, by utilizing a telescoping series method.
Mathematics Subject Classification: 35K05 / 93B07
Key words: Fractional order / Parabolic equations / Analyticity / Observability
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.