Asymptotic integration of the Cauchy problem with countably multiple spectrum (Q1059207)

The authors consider the singularly perturbed Cauchy problem of the form \(L_{\epsilon}u\equiv \epsilon (du/dt)-Au=h(t),\) \(u_{t=0}=\psi\), by the regularization method, where A is a constant non-diagonalizable operator acting in an infinite-dimensional Hilbert space, and has a countable number of multiple spectral points. Under certain conditions, the uniformly valid asymptotic expansion of the solution has been constructed, and the remainder term has been estimated.