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 CMFD, 2017, Volume 63, Issue 2, Pages 316–339 (Mi cmfd322)

Matching spectral and initial-boundary value problems

V. I. Vernadsky Crimean Federal University, 4 Vernadsky Avenue, 295007 Simferopol, Russia

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 of mathematical physics generating matching problems. We prove theorems on unique solvability of a strong solution ranging in the corresponding Hilbert space.

DOI: https://doi.org/10.22363/2413-3639-2017-63-2-316-339

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Bibliographic databases:

UDC: 517.95+517.98

Citation: K. A. Radomirskaya, “Matching spectral and initial-boundary value problems”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 63, no. 2, Peoples' Friendship University of Russia, M., 2017, 316–339

Citation in format AMSBIB
\Bibitem{Rad17} \by K.~A.~Radomirskaya \paper Matching spectral and initial-boundary value problems \inbook Proceedings of the Crimean autumn mathematical school-symposium \serial CMFD \yr 2017 \vol 63 \issue 2 \pages 316--339 \publ Peoples' Friendship University of Russia \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd322} \crossref{https://doi.org/10.22363/2413-3639-2017-63-2-316-339} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3717893}