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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 10
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Articles

Lipschitz stability in an inverse problem for the Kuramoto–Sivashinsky equation

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Pages 2084-2102 | Received 04 May 2012, Accepted 24 Jul 2012, Published online: 29 Aug 2012

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Vo Van Au. (2023) Well- and ill-posedness for a class of the 3D-generalized Kuramoto–Sivashinsky equations. Zeitschrift für angewandte Mathematik und Physik 74:6.
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Kai Cao. (2023) Identification of the time-dependent source term in a Kuramoto–Sivashinsky equation. Journal of Inverse and Ill-posed Problems 0:0.
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Boumediène Chentouf & Baowei Feng. (2023) On the singular limit of a boundary delayed Kuramoto-Sivashinsky-Korteweg-de Vries equation: Well-posedness and stability results. Evolution Equations and Control Theory 0:0, pages 0-0.
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Kai Cao. (2022) Convergence rate analysis of the coefficient identification problems in a Kuramoto–Sivashinsky equation. Inverse Problems 39:1, pages 015006.
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Jamel Ben Amara & Hedi Bouzidi. (2022) Null Boundary Controllability of the Linear Kuramoto–Sivashinsky Equation with Variable Coefficients. Applied Mathematics & Optimization 86:3.
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Boumediène Chentouf & Aissa Guesmia. (2022) Well-posedness and stability results for the Korteweg–de Vries–Burgers and Kuramoto–Sivashinsky equations with infinite memory: A history approach. Nonlinear Analysis: Real World Applications 65, pages 103508.
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Boumediène Chentouf. (2021) On the Exponential Stability of a Nonlinear Kuramoto–Sivashinsky–Korteweg-de Vries Equation with Finite Memory. Mediterranean Journal of Mathematics 19:1.
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Anbu Arivazhagan, Kumarasamy Sakthivel & Natesan Barani Balan. (2021) Inverse source problem for a generalized Korteweg–de Vries equation. Journal of Inverse and Ill-posed Problems 29:6, pages 823-848.
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Nguyen Huy Tuan, Erkan Nane & Dang Duc Trong. (2021) Analysis of a quasi-reversibility method for nonlinear parabolic equations with uncertainty data. Illinois Journal of Mathematics 65:4.
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Boumediène Chentouf. (2021) Well-posedness and exponential stability results for a nonlinear Kuramoto-Sivashinsky equation with a boundary time-delay. Analysis and Mathematical Physics 11:4.
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Yunxia Shang & Shumin Li. (2021) Conditional stability in a backward Cahn–Hilliard equation via a Carleman estimate. Journal of Inverse and Ill-posed Problems 29:2, pages 159-171.
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Diego Gajardo, Alberto Mercado & Juan Carlos Muñoz. (2021) Identification of the anti-diffusion coefficient for the linear Kuramoto-Sivashinsky equation. Journal of Mathematical Analysis and Applications 495:2, pages 124747.
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Patricio Guzmán. (2018) Local Exact Controllability to the Trajectories of the Cahn–Hilliard Equation. Applied Mathematics & Optimization 82:1, pages 279-306.
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Arivazhagan Anbu, Sakthivel Kumarasamy & Barani Balan Natesan. (2020) Lipschitz stability of an inverse problem for the Kawahara equation with damping. AIMS Mathematics 5:5, pages 4529-4545.
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Wensheng Zhang & Zifan Jiang. (2019) Logarithmic stability of an inverse problem for Biot’s consolidation system in poro-elasticity. Journal of Physics Communications 3:11, pages 115022.
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Atsushi Kawamoto. (2018) Lipschitz stability estimates in inverse source problems for a fractional diffusion equation of half order in time by Carleman estimates. Journal of Inverse and Ill-posed Problems 26:5, pages 647-672.
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Mo Chen. (2017) Lipschitz stability in an inverse problem for the Korteweg-de Vries equation on a finite domain. Boundary Value Problems 2017:1.
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Nicolás Carreño & Patricio Guzmán. (2016) On the cost of null controllability of a fourth-order parabolic equation. Journal of Differential Equations 261:11, pages 6485-6520.
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Peng Gao. (2016) A new global Carleman estimate for Cahn–Hilliard type equation and its applications. Journal of Differential Equations 260:1, pages 427-444.
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Peng Gao. (2015) A new global Carleman estimate for the one-dimensional Kuramoto–Sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem. Nonlinear Analysis: Theory, Methods & Applications 117, pages 133-147.
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Peng Gao, Mo Chen & Yong Li. (2015) Observability Estimates and Null Controllability for Forward and Backward Linear Stochastic Kuramoto--Sivashinsky Equations. SIAM Journal on Control and Optimization 53:1, pages 475-500.
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