$\mathbb{R}^n$高阶线性抛物方程的唯一延拓性与能观性

Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (6): 2196-2206.

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Unique Continuation and Observability of Higher-Order Linear Parabolic Equation in $\mathbb{R}^n$

Guojie Zheng¹, Longhan Ye¹, Li Zhu², Xin Yu³^,^*()

¹ College of Mechanical Engineering, Ningbo University of Finance & Economics, Zhejiang Ningbo 315175
² School of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430205
³ Institute of Information Processing and Intelligent Computing, Ningbo Tech University, Zhejiang Ningbo 315100

Received:2025-07-28 Revised:2026-01-23 Online:2026-12-26 Published:2026-08-14
Contact: Xin Yu E-mail:yuxin@zju.edu.cn
Supported by:
NSFC(12171431);Zhejiang Provincial NSF(LY24A010014);Zhejiang Provincial NSF(LZ21A010001)

Abstract

Abstract:

This paper study the observability and unique continuation property of higher-order linear parabolic equations in the whole space. First, the relationship between thick set and spectral inequality is discussed. Secondly, by using spectral inequality, a class of Hölder-type interpolation inequality for the solution of this equation is investigated. Furthermore, with the help of this inequality, the quantitative unique continuation property of this equation in the whole space can be obtained. Finally, the observability estimate for linear higher-order parabolic equations in $\mathbb{R}^n$ is proved by Lebeau-Robbiano strategy.

Key words: observability estimate, higher-order linear parabolic equation, unique continuation property, spectral inequality

CLC Number:

O231.4

Guojie Zheng, Longhan Ye, Li Zhu, Xin Yu. Unique Continuation and Observability of Higher-Order Linear Parabolic Equation in $\mathbb{R}^n$[J].Acta mathematica scientia,Series A, 2026, 46(6): 2196-2206.

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Unique Continuation and Observability of Higher-Order Linear Parabolic Equation in $\mathbb{R}^n$

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