ON A SECOND ORDER DISSIPATIVE ODE IN HILBERT SPACE WITH AN INTEGRABLE SOURCE TERM  

作　　者：Alain Haraux Mohamed Ali Jendoubi 

机构地区：[1]UPMC Univ Paris 06,UMR 7598,Laboratoire Jacques-Louis Lions [2]CNRS,UMR 7598,Laboratoire Jacques-Louis Lions [3]Facult des Sciences de Bizerte,Dpartement de Mathmatiques

出　　处：《Acta Mathematica Scientia》2012年第1期155-163,共9页数学物理学报（B辑英文版）

基　　金：support by the France-Tunisia cooperation under the auspices of the CNRS/DGRSRT agreement No. 08/R 15-06:Systèmes dynamiques et équationsd'évolution;Laboratoire Jacques-Louis Lions under the auspices of the Fondation Sciences Mathematiques de Paris

摘　　要：Asymptotic behaviour of solutions is studied for some second order equations including the model casex（t） ＋γx（t） ＋ ↓△φb（x（t）） = h（t） with γ 〉 0 and h ∈ L1（O, ＋∞; H）, φ being continuouly differentiable with locally Lipschitz continuous gradient and bounded from below. In particular when φ is convex, all solutions tend to minimize the potential φ as time tends to infinity and the existence of one bounded trajectory implies the weak convergence of all solutions to equilibrium points.Asymptotic behaviour of solutions is studied for some second order equations including the model casex（t） ＋γx（t） ＋ ↓△φb（x（t）） = h（t） with γ 〉 0 and h ∈ L1（O, ＋∞; H）, φ being continuouly differentiable with locally Lipschitz continuous gradient and bounded from below. In particular when φ is convex, all solutions tend to minimize the potential φ as time tends to infinity and the existence of one bounded trajectory implies the weak convergence of all solutions to equilibrium points.

关 键 词：dissipative dynamical system asymptotic behaviour gradient system heavyball with friction 

分 类 号：O177.1[理学—数学] O177.6[理学—基础数学]