Infinite speed of propagation and unique continuation for solutions of the drift-diffusion equation via Carleman estimates

Imaida, Yuuki; Shibata, Kosuke; Sugiyama, Yoshie

Journal of Differential Equations, 2025, 448, 113670

Number of Access:10（2025-10-27 03:24 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/102787

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Title
Infinite speed of propagation and unique continuation for solutions of the drift-diffusion equation via Carleman estimates
Creator
CreatorName
Imaida, Yuuki
CreatorName
Shibata, Kosuke
NRID
1000060308210 1000060308210
researchmap permalink
sugiyamayoshie sugiyamayoshie
Scopus Author ID
9433451100 9433451100
CreatorName
Sugiyama, Yoshie
Subject
Carleman estimates
Drift-diffusion equation
Infinite speed of propagation
Two-sphere one-cylinder inequality
Unique continuation theorem
Description
Imaida Y., Shibata K., Sugiyama Y.. Infinite speed of propagation and unique continuation for solutions of the drift-diffusion equation via Carleman estimates. Journal of Differential Equations 448, 113670 (2025); https://doi.org/10.1016/j.jde.2025.113670.
Abstract
Through the use of Carleman estimates, we investigate the drift-diffusion equation and demonstrate the infinite propagation of its solutions, considering both the parabolic-parabolic and parabolic-elliptic forms. A primary result is a Unique Continuation Theorem, which states that if a solution vanishes on a non-empty open set, it must vanish throughout the whole space Rn. The proof relies on the Two-Sphere One-Cylinder Inequality, derived from the Carleman estimates. As a consequence, we show the infinite speed of propagation for solutions: even if the initial data has compact support, the solution corresponding to this initial data will instantly extend to cover the whole space Rn. This result highlights a solution structure typical of linear diffusion equations of the heat type, where solutions exhibit immediate and global propagation.
Publisher
Elsevier Inc.
Source Title
Journal of Differential Equations
Volume (Issue)
448
Page
113670
Date of Issued
2025-12-15
Language
English
Handle URL
https://hdl.handle.net/11094/102787
PISSN
00220396
eISSN
10902732
Relation.isIdenticalTo
DOI (Publisher Version)
https://doi.org/10.1016/j.jde.2025.113670
Access Rights
open access
CopyRight
This article is licensed under a Creative Commons Attribution 4.0 International License.
© 2025 The Authors
oaire:version
Version of Record
Category
学術雑誌論文 Journal Article