Carleman Estimates for Second Order Parabolic Operators and Applications, a Unified Approach

Fu, Xiaoyu; Lü, Qi; Zhang, Xu

doi:10.1007/978-3-030-29530-1_3

Cited by 2 publications

(1 citation statement)

References 46 publications

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“…As we said before, the main tool for establishing the conditional stability is a new global Carleman estimate for (1.1). Carleman estimates are widely applied to many inverse problems for deterministic partial differential equations (see [2,8,9] and the rich references therein). Recently, Carleman estimates are also introduced to solve inverse problems for stochastic partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Determination of the solution of a stochastic parabolic equation by the terminal value

Dou¹,

Du²

2022

Inverse Problems

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This paper studies the inverse problem of determination the history for a stochastic diﬀusion process, by means of the value at the ﬁnal time T . By establishing a new Carleman estimate, the conditional stability of the problem is proven. Based on the idea of Tikhonov method, a regularized solution is proposed. The analysis of the existence and uniqueness of the regularized solution, and proof for error estimate under an aproior assumption are present. Numerical veriﬁcation of the regularization, including numerical algorithm and examples are also illustrated.

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Section: Introductionmentioning

confidence: 99%

Determination of the solution of a stochastic parabolic equation by the terminal value

Dou¹,

Du²

2022

Inverse Problems

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The Bang–Bang Property of Time-Varying Optimal Time Control for Null Controllable Heat Equation

Yang

Guo

Gui

et al. 2019

J Optim Theory Appl

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In this paper, we consider bang-bang property for a kind of time-varying time optimal control problem of null controllable heat equation. The study is a continuation of a recent work (Chen et al. in Syst Control Lett 112:18-23, 2018), where an approximate null controllable heat equation was considered. We first establish the equivalence between optimal norm control and optimal time control and then prove the existence of the optimal norm control and of the optimal time control. The time-varying bangbang property for the optimal time control is finally established.

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Carleman Estimates for Second Order Parabolic Operators and Applications, a Unified Approach

Cited by 2 publications

References 46 publications

Determination of the solution of a stochastic parabolic equation by the terminal value

Determination of the solution of a stochastic parabolic equation by the terminal value

The Bang–Bang Property of Time-Varying Optimal Time Control for Null Controllable Heat Equation

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