Large-Time Behavior of Solutions to Evolution Equations

Large-time behavior of solutions to abstract differential equations is studied. The results give sufficient condition for the solution to an abstract dynamical system (evolution problem) not to exhibit chaotic behavior. The corresponding evolution problem is * u ˙  =  A ( t ) u  +  F ( t , u )  +  b ( t ) ,      t  ≥  0 ;      u ( 0 )  =  u 0 .