In this paper we consider the Elastic membrane equation：with memory term and nonlinear boundary damping： Under some appropriate assumptions on the relaxation function h and with certain initial data, the global exis...In this paper we consider the Elastic membrane equation：with memory term and nonlinear boundary damping： Under some appropriate assumptions on the relaxation function h and with certain initial data, the global existence of solutions ：and a general decay for the energy are established using the multiplier technique. Also, ＇we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a nonlinear damping.展开更多
In this paper,we consider a nonlinear wave equation with nonlocal damping and nonlinear boundary damping.We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary dampin...In this paper,we consider a nonlinear wave equation with nonlocal damping and nonlinear boundary damping.We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping by using of the multiplier technique from the idea of Martinez[1],Our result extends and improves the result in the literature such as the work by Louredo,Ferreira de Araujo and Mi-randain[2]in which only exponential energy decay is considered.Furthermore,we get also the energy decay for the equation with nonlocal damping only but without nonlinear boundary damping.展开更多
In this article, we study the weak dissipative Kirchhoff equation under nonlinear damping on the boundary We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary dampi...In this article, we study the weak dissipative Kirchhoff equation under nonlinear damping on the boundary We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping. Our result extends and improves some results in the literature such as the work by Zhang and Miao （2010） in which only exponential energy decay is considered and the work by Zhang and Huang （2014） where the energy decay has been not considered.展开更多
An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system （FPSO system）. Finite water depth Green function and higher-order boundar...An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system （FPSO system）. Finite water depth Green function and higher-order boundary ele- ment method are used to solve integral equation. Numeri- cal results about added mass and damping are presented for odd and even mode motions of FPSO. The results show ro- bust convergence in high frequency range and can be used in wave load analysis for FPSO designing and operation.展开更多
In this paper, we consider the partial differential equation of an elastic beam with structuraldamping by boundary feedback control. First, we prove this closed system is well--posed; then weestablish tbe exponential ...In this paper, we consider the partial differential equation of an elastic beam with structuraldamping by boundary feedback control. First, we prove this closed system is well--posed; then weestablish tbe exponential stability for this elastic system by using a theorem whichbelongs to F. L.Huang; finally, we discuss the distribution and multiplicity of the spectrum of this system. Theseresults are very important and useful in practical applications.展开更多
In this paper we prove that every compact invariant subset■associated with the semigroup{Sn,k(t)}t≥0 generated by wave equations with variable damping,either in the interior or on the boundary of the domainΩwhereΩ...In this paper we prove that every compact invariant subset■associated with the semigroup{Sn,k(t)}t≥0 generated by wave equations with variable damping,either in the interior or on the boundary of the domainΩwhereΩ■R^3 is a smooth bounded domain,in H^10(Ω)×L^2(Ω)is in fact bounded in D(B0)×H^10(Ω)As an application of our results,we obtain the upper-semicontinuity for global attractor of the weakly damped semilinear wave equation in the norm of H^1(Ω)×L^2(Ω)when the interior variable damping converges to theboundary damping in the sense of distributions.展开更多
文摘In this paper we consider the Elastic membrane equation：with memory term and nonlinear boundary damping： Under some appropriate assumptions on the relaxation function h and with certain initial data, the global existence of solutions ：and a general decay for the energy are established using the multiplier technique. Also, ＇we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a nonlinear damping.
基金supported by National Natural Science Foundation of China(Nos.11601122,11801145)。
文摘In this paper,we consider a nonlinear wave equation with nonlocal damping and nonlinear boundary damping.We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping by using of the multiplier technique from the idea of Martinez[1],Our result extends and improves the result in the literature such as the work by Louredo,Ferreira de Araujo and Mi-randain[2]in which only exponential energy decay is considered.Furthermore,we get also the energy decay for the equation with nonlocal damping only but without nonlinear boundary damping.
文摘In this article, we study the weak dissipative Kirchhoff equation under nonlinear damping on the boundary We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping. Our result extends and improves some results in the literature such as the work by Zhang and Miao （2010） in which only exponential energy decay is considered and the work by Zhang and Huang （2014） where the energy decay has been not considered.
基金supported by the Fundamental Research Funds forthe Central Universities (DVT10LK43)the Returned Overseas Chinese Scholars,State Education Ministry (2007[24])
文摘An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system （FPSO system）. Finite water depth Green function and higher-order boundary ele- ment method are used to solve integral equation. Numeri- cal results about added mass and damping are presented for odd and even mode motions of FPSO. The results show ro- bust convergence in high frequency range and can be used in wave load analysis for FPSO designing and operation.
文摘In this paper, we consider the partial differential equation of an elastic beam with structuraldamping by boundary feedback control. First, we prove this closed system is well--posed; then weestablish tbe exponential stability for this elastic system by using a theorem whichbelongs to F. L.Huang; finally, we discuss the distribution and multiplicity of the spectrum of this system. Theseresults are very important and useful in practical applications.
基金The first author is supported by“the Fundamental Research Funds for the Central Universities”,NO.NS2020058was supported by the National Natural Science Foundation of China under Grant 11501289.
文摘In this paper we prove that every compact invariant subset■associated with the semigroup{Sn,k(t)}t≥0 generated by wave equations with variable damping,either in the interior or on the boundary of the domainΩwhereΩ■R^3 is a smooth bounded domain,in H^10(Ω)×L^2(Ω)is in fact bounded in D(B0)×H^10(Ω)As an application of our results,we obtain the upper-semicontinuity for global attractor of the weakly damped semilinear wave equation in the norm of H^1(Ω)×L^2(Ω)when the interior variable damping converges to theboundary damping in the sense of distributions.
