Convergent families of approximate inertial manifolds for nonautonomous evolution equations
This paper deals with the long time behaviour of non-autonomous infinite-dimensional dynamical systems. Theoretically the inertial manifold cannot be expressed explicitly. To overcome this drawback, the authors construct a convergent family of approximate inertial manifolds \(M_N\), \(N=1,2,\dots\), which can be expressed explicitly. They show that when \(N\to +\infty\), the \(M_N\) approximate the exact inertial manifolds, the existence of which is guaranteed by the spectral gap condition.
scientific article; zbMATH DE number 1292963
scientific article