Asymptotic stability for abstract evolution equations and applications to partial differential systems (Q1389814)

The authors study asymptotic stability, as time tends to infinity, of abstract evolution equations of the form \[ [P(u''(t))]^\prime+A(u(t))+\rho(t)A(u''(t))+ Q(t,u''(t))+F(u(t))=0,\quad t\in I, \] where \(I=[0,\infty)\), \(\rho\in L^1_{\text{loc}}(I\to {\mathbb{R}}^+_0)\), \(A,F,P\) and \(Q\) are nonlinear operators on suitable Banach spaces. Applications to damped wave systems are discussed.