具有箝位边界条件的N维板方程的Carleman估计及其应用

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-04-10 DOI:10.1016/j.jmaa.2025.129583

Alex Imba , Alberto Mercado

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引用次数: 0

摘要

在本文中，我们为在N大于或等于2的RN的有界域中作用的Euler-Bernoulli板算子建立了一个新的全局Carleman估计，其中施加了固定的边界条件。我们用部分边界的观测值得到一个加权估计。作为Carleman不等式的一个应用，我们得到了在任意正时刻从边界测量中恢复系统源项空间部分的反问题的一个Lipschitz稳定性结果。

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Carleman estimates for an N− dimensional plate equation with clamped boundary conditions and applications

In this paper, we establish a new global Carleman estimate for the Euler-Bernoulli plate operator acting in a bounded domain of

R^{N}

with

N ⩾ 2

, in which clamped boundary conditions have been imposed. We obtain a weighted estimate with observations in part of the boundary. As an application of the Carleman inequality, we obtain a Lipschitz stability result for the inverse problem of recovering the spatial part of the source term of the system from boundary measurements at any arbitrary positive time.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.