非自治退化 PDE 的无效可控性和卡勒曼估计：气候学应用

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-10-28 DOI:10.1016/j.jmaa.2024.128984

Mohammad Akil , Genni Fragnelli , Sarah Ismail

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引用次数: 0

摘要

受布迪科-塞勒模型的启发，我们考虑了非自治退化抛物方程。首先，我们利用加藤定理证明了此类问题的好求性。然后，通过对非均质非自治邻接问题进行新的卡勒曼估计，我们推导出原始问题的空可控性。我们还考虑了一些线性和半线性扩展问题。最后，我们将获得的可控性结果应用于引言中给出的布迪科-塞勒模型。

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Null-controllability and Carleman estimates for non-autonomous degenerate PDEs: A climatological application

Inspired by a Budyko-Seller model, we consider non-autonomous degenerate parabolic equations. As a first step, using Kato's Theorem we prove the well-posedness of such problems. Then, obtaining new Carleman estimates for the non-homogeneous non-autonomous adjoint problems, we deduce null-controllability for the original ones. Some linear and semilinear extensions are also considered. We conclude the paper applying the obtained controllability result to the Budyko-Seller model given in the introduction.

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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.