title: Matching Spectral and Initial-Boundary Value Problems
abstract: Based on the approach to abstract matching boundary-value problems introduced in [18], we consider matching spectral problems for one and two domains. We study in detail the arising operator pencil with self-adjoint operator coeﬃcients. This pencil acts in a Hilbert space and depends on two parameters. Both possible cases are considered, where one parameter is spectral and the other is ﬁxed, and properties of solutions are obtained depending on this. Also we study initial-boundary value problems
journal: Contemporary Mathematics Fundamental Directions