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学者姓名：马牧
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Abstract ：
This paper is concerned with the Cauchy problem for a weakly dissipative 3-component Camassa-Holm system. We first obtain the local well-posedness of solutions by using Kato's theory. We then derive the wave breaking mechanism of solutions, and give two wave breaking criteria for solutions by the method of characteristic and convolution estimates. Finally, we prove that if the initial data with their derivatives of the system exponentially decay at infinity, then the corresponding solution also exponentially decays at infinity.
Keyword ：
Persistence property Persistence property Shallow water wave Shallow water wave Wave breaking Wave breaking
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| GB/T 7714 | Zhou, Yonghui , Li, Xiaowan , Ma, Mu . Wave breaking and persistence property of solutions for a weakly dissipative 3-component Camassa-Holm system [J]. | MONATSHEFTE FUR MATHEMATIK , 2024 , 207 (1) : 151-174 . |
| MLA | Zhou, Yonghui 等. "Wave breaking and persistence property of solutions for a weakly dissipative 3-component Camassa-Holm system" . | MONATSHEFTE FUR MATHEMATIK 207 . 1 (2024) : 151-174 . |
| APA | Zhou, Yonghui , Li, Xiaowan , Ma, Mu . Wave breaking and persistence property of solutions for a weakly dissipative 3-component Camassa-Holm system . | MONATSHEFTE FUR MATHEMATIK , 2024 , 207 (1) , 151-174 . |
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Abstract ：
In this paper, based on the average dwell time (ADT) switching policy, the issue of secure control, for discrete-time switched positive systems, is studied under false data injection (FDI) attacks. Attacks are considered as a unforeseen behavior that occur randomly through network communication, and can be appropriately characterized by Bernoulli random variables. Feedback controllers are developed for individual subsystems, a suitable copositive Lyapunov-Krasovskii functional (LKF) is built, and the stochastic stability criterion of switched positive delayed systems under FDI attacks is also established. Eventually, an academic example is provided to confirm the efficacy of the suggested scheme.
Keyword ：
ADT ADT FDI attacks FDI attacks stabilization stabilization Switched positive systems Switched positive systems
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| GB/T 7714 | Xu, Jincan , Ma, Mu , Wang, Peng et al. Secure Control for Switched Positive Systems Against False Data Injection Attacks [J]. | 39TH YOUTH ACADEMIC ANNUAL CONFERENCE OF CHINESE ASSOCIATION OF AUTOMATION, YAC 2024 , 2024 : 945-949 . |
| MLA | Xu, Jincan et al. "Secure Control for Switched Positive Systems Against False Data Injection Attacks" . | 39TH YOUTH ACADEMIC ANNUAL CONFERENCE OF CHINESE ASSOCIATION OF AUTOMATION, YAC 2024 (2024) : 945-949 . |
| APA | Xu, Jincan , Ma, Mu , Wang, Peng , Sun, Yaowei . Secure Control for Switched Positive Systems Against False Data Injection Attacks . | 39TH YOUTH ACADEMIC ANNUAL CONFERENCE OF CHINESE ASSOCIATION OF AUTOMATION, YAC 2024 , 2024 , 945-949 . |
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In this paper, we investigate the existence of multiple nontrivial periodic solutions for an asymptotically linear wave equation with x-dependent coefficients. Such a mathematical model can be derived from the forced vibrations of a nonhomogeneous string and propagation of seismic waves in nonisotropic media. By constructing a suitable function space, we characterize the problem as a variational problem, and then we prove that there are at least three nontrivial periodic solutions via variational methods.
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| GB/T 7714 | Wei, Hui , Ma, Mu , Ji, Shuguan . Multiple periodic solutions for an asymptotically linear wave equation with x-dependent coefficients [J]. | JOURNAL OF MATHEMATICAL PHYSICS , 2021 , 62 (11) . |
| MLA | Wei, Hui et al. "Multiple periodic solutions for an asymptotically linear wave equation with x-dependent coefficients" . | JOURNAL OF MATHEMATICAL PHYSICS 62 . 11 (2021) . |
| APA | Wei, Hui , Ma, Mu , Ji, Shuguan . Multiple periodic solutions for an asymptotically linear wave equation with x-dependent coefficients . | JOURNAL OF MATHEMATICAL PHYSICS , 2021 , 62 (11) . |
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Abstract ：
In this paper, we consider the one-dimensional Kirchhoff equation with x-dependent coefficients under the spatial periodic conditions, which models the forced vibrations of an inhomogeneous string in presence of a time periodic external forcing with period 2 pi/omega and amplitude E>0. By using the Lyapunov-Schmidt reduction and the Nash-Moser iteration technique, we obtain the existence, regularity and local uniqueness of time periodic solutions with period 2 pi/omega and order E. Such results hold for parameters (omega ,E) in a positive measure Cantor set that has asymptotically full measure as the amplitude E goes to zero.
Keyword ：
Kirchhoff equation Kirchhoff equation Nash-Moser iteration Nash-Moser iteration Time periodic solutions Time periodic solutions
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| GB/T 7714 | Ma, Mu , Ji, Shuguan . Time periodic solutions of one-dimensional forced Kirchhoff equations with x-dependent coefficients under spatial periodic conditions [J]. | ANALYSIS AND MATHEMATICAL PHYSICS , 2019 , 9 (4) : 2345-2366 . |
| MLA | Ma, Mu et al. "Time periodic solutions of one-dimensional forced Kirchhoff equations with x-dependent coefficients under spatial periodic conditions" . | ANALYSIS AND MATHEMATICAL PHYSICS 9 . 4 (2019) : 2345-2366 . |
| APA | Ma, Mu , Ji, Shuguan . Time periodic solutions of one-dimensional forced Kirchhoff equations with x-dependent coefficients under spatial periodic conditions . | ANALYSIS AND MATHEMATICAL PHYSICS , 2019 , 9 (4) , 2345-2366 . |
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