Convergent families of inertial manifolds for convergent approximations (Q1370358)

The object of study is the equation on a Hilbert space \(H : du/dt+Au+f(u)=0\), where \(A\) is a linear operator which is positive, selfadjoint, unbounded, and has a compact inverse. The nonlinearity is taken to be a globally bounded Lipschitz map from \(D(A^\alpha)\) into \(D(A^\beta)\) with \(0\leq\alpha - \beta<1\) and with support contained in a ball in \(D(A^\alpha)\). The author shows that a sequence of (suitably uniform) inertial manifolds for a family of approximations converges to an inertial manifold for the limiting problem, without imposing any additional assumptions.