The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered.It is proved that the system is exponentially stabilizable.The frequency domain method and the multipl...The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered.It is proved that the system is exponentially stabilizable.The frequency domain method and the multiplier technique are applied.展开更多
This paper studies the stabilization problem of uniform Euler-Bernoulli beam with a nonlinear locally distributed feedback control. By virtue of nonlinear semigroup theory, energy-perturbed approach and polynomial mul...This paper studies the stabilization problem of uniform Euler-Bernoulli beam with a nonlinear locally distributed feedback control. By virtue of nonlinear semigroup theory, energy-perturbed approach and polynomial multiplier skill, the authors show that, corresponding to the different values of the parameters involved in the nonlinear locally distributed feedback control, the energy of the beam under the proposed feedback decays exponentially or in negative power of time t as t →∞.展开更多
The stabilization problem of a nonuniform Timoshenko beam system With coupled locally distributed feedback controls is studied. First, by proving the uniqueness of the solution to the related ordinary differential equ...The stabilization problem of a nonuniform Timoshenko beam system With coupled locally distributed feedback controls is studied. First, by proving the uniqueness of the solution to the related ordinary differential equations, we establish the asymptotic decay of the energy corresponding to the closed loop system. Then, by virtue of piecewise multiplier method, we prove the exponential decay of the closed loop system.展开更多
In this article, we study the stabilization problem of a nonuniform Euler-Bernoulli beam with locally distributed feedbacks. Firstly, using the semi-group theory, we establish the well-posedness of the associated clos...In this article, we study the stabilization problem of a nonuniform Euler-Bernoulli beam with locally distributed feedbacks. Firstly, using the semi-group theory, we establish the well-posedness of the associated closed loop system. Then by proving the uniqueness of the solution of a related ordinary differential equations, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise frequency domain multiplier method, we prove that the corresponding closed loop system can be exponentially stabilized by only one of the two distributed feedback controls proposed in this paper.展开更多
The near-surface temperatures in the Arctic are increasing at more than twice the global average rate,a phenomenon known as Arctic amplification(AA).In recent years,numerous studies using ground-based and satellite ob...The near-surface temperatures in the Arctic are increasing at more than twice the global average rate,a phenomenon known as Arctic amplification(AA).In recent years,numerous studies using ground-based and satellite observations,along with model simulations,have explored the potential mechanisms behind AA,offering a variety of observational evidence and theoretical explanations.Although the understanding of AA drivers has improved,significant uncertainties remain in quantifying the contributions of different influential factors.On the basis of the latest research,this article thoroughly examines the factors driving rapid warming in the Arctic,including local feedbacks,atmospheric circulation,ocean currents,and aerosols,and compares quantitative results across studies.The analysis highlights the complex interplay of multiple factors contributing to AA,with no clear consensus on the relative contributions of each driver.Finally,the article underscores key challenges in current research,emphasizing the need for more reliable observational data,a deeper understanding of AA mechanisms,improved model parameterizations,and the disentanglement of interactions among driving factors,all of which are essential for future investigations.展开更多
基金Supported partially by the NSFC and the Science Foundation of China State Education Commission.
文摘The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered.It is proved that the system is exponentially stabilizable.The frequency domain method and the multiplier technique are applied.
基金This research is supported by the National Science Foundation of China under Grant Nos. 10671166 and 60673101.
文摘This paper studies the stabilization problem of uniform Euler-Bernoulli beam with a nonlinear locally distributed feedback control. By virtue of nonlinear semigroup theory, energy-perturbed approach and polynomial multiplier skill, the authors show that, corresponding to the different values of the parameters involved in the nonlinear locally distributed feedback control, the energy of the beam under the proposed feedback decays exponentially or in negative power of time t as t →∞.
基金This research is partially supported by the Research Committee of the Hong Kong Polytechnic University by the Science Foundation of China Geosciences University (Beijing) (200304).
文摘The stabilization problem of a nonuniform Timoshenko beam system With coupled locally distributed feedback controls is studied. First, by proving the uniqueness of the solution to the related ordinary differential equations, we establish the asymptotic decay of the energy corresponding to the closed loop system. Then, by virtue of piecewise multiplier method, we prove the exponential decay of the closed loop system.
基金Supported by Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (No. 201102)Beijing Natural Science Foundation (No. 1052007)
文摘In this article, we study the stabilization problem of a nonuniform Euler-Bernoulli beam with locally distributed feedbacks. Firstly, using the semi-group theory, we establish the well-posedness of the associated closed loop system. Then by proving the uniqueness of the solution of a related ordinary differential equations, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise frequency domain multiplier method, we prove that the corresponding closed loop system can be exponentially stabilized by only one of the two distributed feedback controls proposed in this paper.
基金supported by the National Natural Science Foudation of Distinguished Young Scholars(Grant No.41925022)。
文摘The near-surface temperatures in the Arctic are increasing at more than twice the global average rate,a phenomenon known as Arctic amplification(AA).In recent years,numerous studies using ground-based and satellite observations,along with model simulations,have explored the potential mechanisms behind AA,offering a variety of observational evidence and theoretical explanations.Although the understanding of AA drivers has improved,significant uncertainties remain in quantifying the contributions of different influential factors.On the basis of the latest research,this article thoroughly examines the factors driving rapid warming in the Arctic,including local feedbacks,atmospheric circulation,ocean currents,and aerosols,and compares quantitative results across studies.The analysis highlights the complex interplay of multiple factors contributing to AA,with no clear consensus on the relative contributions of each driver.Finally,the article underscores key challenges in current research,emphasizing the need for more reliable observational data,a deeper understanding of AA mechanisms,improved model parameterizations,and the disentanglement of interactions among driving factors,all of which are essential for future investigations.
