Existence and asymptotic stability for evolution problems on manifolds with damping and source terms

One considers the nonlinear evolution equation with source and damping terms

     

Nonlinear Internal Damping of Wave Equations with Variable Coefficients

For wave equations with variable coefficients on regions which are not necessarily smooth, we study the energy decay rate when a nonlinear damping is applied on a suitable subrigion.     

Energy decay rates for solutions of the wave equations with nonlinear damping in exterior domain

In this paper we study the behaviors of the energy of solutions of the wave equations with localized nonlinear damping in exterior domains.     

一类机器人系统的最优控制

本文通过把结构阻尼系数当作控制变量来讨论一类弹性机器人系统的最优控制问题 ,并利用Banach空间几何性质证明了最优控制元的存在唯一性     

A CLASS OF r-POINT (r+1)ST-ORDER A-STABLE ONE-BLOCK METHODS WITH DAMPING AT THE INFINITE POINT

1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｓｏｌｖｉｎｇｓｔｉｆｆｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｓｙｓｔｅｍｓｏｆＯＤＥｓｙ′=ｆ(ｙ) ,ｙ(ｔ0 ) =ｙ0 ,ｔ0 <ｔ≤Ｔ ,ｙ0 ,ｙ∈Ｒｍ,ｆ :Ω Ｒｍ →Ｒｍ (1 .1 )ｍａｎｙｐａｒｔｉｃｕｌａｒｏｎｅ ｂｌｏｃｋｍｅｔｈｏｄｓｏｆｔｈｅｆｏｒｍＹｎ+1= ＡＹｎ+ｈ( Ｂ0 Ｆ(Ｙｎ) + Ｂ1Ｆ(Ｙｎ+1) ) , Ａ =Ａ Ｉｍ, Ｂｉ=Ｂｉ Ｉｍ,Ａ ,Ｂｉ∈Ｒｒ×ｒ,Ｙｎ =(ＹＴｎｒ,… ,ｙＴ(ｎ+1)ｒ- 1) Ｔ,Ｆ(Ｙｎ) =(ｆＴ(ｙｎｒ) ,… ,ｆＴ(ｙ(ｎ+1)ｒ- 1) ) Ｔ,ｙｊ≈ ｙ(ｔｊ) ,…     

带阻尼项的三阶脉冲微分方程的振动性与渐近性

解决了一类带阻尼项的三阶脉冲微分方程的非振动解与其一阶、二阶导数的符号关系,用迭代法得到其振动性与渐近性的判别准则,并举例说明准则的有效性.     

具有阻尼的半线性波动方程解的衰减估计

研究具有阻尼的半线性波动方程的初边值问题u_(tt)-△u+βu_t=|u|~(p-1)u,x∈Ω,t>0u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈Ωu|_((?)Ω)=0,t≥0其中γ为正常数,Ω■R~n为有界域,当n≥3时,1相似文献   

Oscillation theorem for superlinear second order damped differential equations

In this paper, we are concerned with the oscillation of second order superlinear differential equations of the form

(a(t)y^′(t))^′+p(t)y^′(t)+q(t)f(y(t))=0.     

On a wave equation with supercritical interior and boundary sources and damping terms

This article addresses nonlinear wave equations with supercritical interior and boundary sources, and subject to interior and boundary damping. The presence of a nonlinear boundary source alone is known to pose a significant difficulty since the linear Neumann problem for the wave equation is not, in general, well‐posed in the finite‐energy space H¹(Ω) × L₂(?Ω) with boundary data in L₂ due to the failure of the uniform Lopatinskii condition. Further challenges stem from the fact that both sources are non‐dissipative and are not locally Lipschitz operators from H¹(Ω) into L₂(Ω), or L₂(?Ω). With some restrictions on the parameters in the model and with careful analysis involving the Nehari Manifold, we obtain global existence of a unique weak solution, and establish exponential and algebraic uniform decay rates of the finite energy (depending on the behavior of the dissipation terms). Moreover, we prove a blow up result for weak solutions with nonnegative initial energy.