Abstract:
Based on the generalized Green formula for a sesquilinear nonsymmetric form for the Laplace operator, we consider spectral nonself-adjoint problems. Some of them are similar to classical problems while the other arise in problems of hydrodynamics, diffraction, and problems with surface dissipation of energy. Properties of solutions of such problems are considered. Also we study initial-boundary value problems generating considered spectral problems and prove theorems on correct solvability of such problems on any interval of time.
Citation:
N. D. Kopachevskii, A. R. Yakubova, “On some problems generated by a sesquilinear form”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 63, no. 2, Peoples' Friendship University of Russia, M., 2017, 278–315
\Bibitem{KopYak17}
\by N.~D.~Kopachevskii, A.~R.~Yakubova
\paper On some problems generated by a~sesquilinear form
\inbook Proceedings of the Crimean autumn mathematical school-symposium
\serial CMFD
\yr 2017
\vol 63
\issue 2
\pages 278--315
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd321}
\crossref{https://doi.org/10.22363/2413-3639-2017-63-2-278-315}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3717892}
Linking options:
https://www.mathnet.ru/eng/cmfd321
https://www.mathnet.ru/eng/cmfd/v63/i2/p278
This publication is cited in the following 3 articles:
V. I. Voititskii, M. A. Muratov, Yu. S. Pashkova, P. A. Starkov, T. A. Suslina, D. O. Tsvetkov, “Pamyati Nikolaya Dmitrievicha Kopachevskogo, matematika i cheloveka”, Posvyaschaetsya pamyati professora N.D. Kopachevskogo, SMFN, 67, no. 2, Rossiiskii universitet druzhby narodov, M., 2021, 193–207
A. R. Yakubova, “O spektralnykh i evolyutsionnykh zadachakh, porozhdennykh polutoralineinoi formoi”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 66, no. 2, Rossiiskii universitet druzhby narodov, M., 2020, 335–371
N. D. Kopachevskii, A. R. Yakubova, “On Some Problems Generated by a Sesquilinear Form”, J Math Sci, 250:4 (2020), 622
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