A new global Carleman estimate for the one-dimensional Kuramoto-Sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem

Gao Peng

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A new global Carleman estimate for the one-dimensional Kuramoto-Sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem

机译：一维Kuramoto-Sivashinsky方程的新的全局Carleman估计及其在精确控制轨迹和逆问题中的应用

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摘要

In this paper, we establish a new global Carleman estimate for the linearized Kuramoto-Sivashinsky equation which is a one-parameter Carleman estimate. Based on this estimate, we can obtain the local exact controllability to the trajectories and Lipschitz stability in an inverse problem for the Kuramoto-Sivashinsky equation. (C) 2015 Elsevier Ltd. All rights reserved.

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《Nonlinear Analysis: An International Multidisciplinary Journal》 |2015年第null期|共15页
作者
Gao Peng;
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正文语种 eng
中图分类数学分析;
关键词
Carleman estimate; Kuramoto-Sivashinsky equation; Controllability; Inverse problem;

机译：Carleman估计;Kuramoto-Sivashinsky方程;可控制性;反问题;

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专利

1. 广义Kuramoto-Sivashinsky方程强解的全局吸引子的存在性 [J] . 王素云, 牟录贵, 张艳红数学季刊（英文版） . 2008,第001期
2. A new global Carleman estimate for the one-dimensional Kuramoto-Sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem [J] . Gao Peng Nonlinear Analysis: An International Multidisciplinary Journal . 2015,第Null期

机译：一维Kuramoto-Sivashinsky方程的新的全局Carleman估计及其在精确控制轨迹和逆问题中的应用
3. Global Carleman estimates for the linear stochastic Kuramoto-Sivashinsky equations and their applications [J] . Gao Peng Journal of Mathematical Analysis and Applications . 2018,第1期

机译：全球Carleman估计线性随机Kuramoto-Sivashinsky方程及其应用
4. Sharp Carleman estimates for singular parabolic equations and application to Lipschitz stability in inverse source problems [Inégalités fines de Carleman pour des problèmes paraboliques singuliers et application à des problèmes inverses] [J] . Vancostenoble J. Comptes rendus. Mathematique . 2010,第13a14期

机译：奇异抛物线方程组的Sharp Carleman估计及其在逆源问题中的Lipschitz稳定性[奇异抛物线问题的Carleman精细不等式及其在逆问题中的应用]
5. Lie Symmetry Analysis and Exact Solutions for the Coupled Kuramoto-Sivashinsky Equations [C] . Yan Fang, Hua Cuncai, Liu Haihong, 2011 Fourth International Workshop on Chaos-Fractals Theories and Applications . 2011

机译：耦合的Kuramoto-Sivashinsky方程的Lie对称性分析和精确解
6. Geometric optics, convex functions, Carleman estimates and interfaces in the boundary control of the wave equation [D] . Galbraith, Michael Lee. 2004

机译：几何光学，凸函数，CORLEMAN估计和波浪方程边界控制中的界面
7. High-Resolution Protein Structure Determination Starting with a Global Fold Calculated from Exact Solutions to the RDC Equations [O] . Jianyang Zeng, Jeffrey Boyles, Chittaranjan Tripathy, -1

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8. Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem [O] . Benabdallah Assia, Dermenjian Yves, Le Rousseau Jérôme 2007

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9. Global Uniqueness for a Coefficient Inverse Problem for the Non- Stationary Transport Equation via Carleman Estimate. [R] . Klibanov, M. V., Pamyatnykh, S. E. 2006

机译：基于Carleman估计的非平稳输运方程系数反问题的全局唯一性。

A new global Carleman estimate for the one-dimensional Kuramoto-Sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem

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