Geodesic
Matching spectral and initial-boundary value problems
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 63 (2017) no. 2, pp. 316-339

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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 of mathematical physics generating matching problems. We prove theorems on unique solvability of a strong solution ranging in the corresponding Hilbert space. 
@article{CMFD_2017_63_2_a5,
     author = {K. A. Radomirskaya},
     title = {Matching spectral and initial-boundary value problems},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {316--339},
     publisher = {mathdoc},
     volume = {63},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2017_63_2_a5/}
}
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K. A. Radomirskaya. Matching spectral and initial-boundary value problems. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 63 (2017) no. 2, pp. 316-339. http://geodesic.mathdoc.fr/item/CMFD_2017_63_2_a5/