Abstract:
Boundary-value problems for fourth-order linear partial differential equations of hyperbolic and composite types are studied. The method of energy inequalities and averaging operators with variable step is used to prove existence and uniqueness theorems for strong solutions. The Riesz theorem on the representation of linear continuous functionals in Hilbert spaces is used to prove the existence and uniqueness theorems for generalized solutions.
Citation:
V. I. Korzyuk, O. A. Konopel'ko, E. S. Cheb, “Boundary-value problems for fourth-order equations of hyperbolic and composite types”, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, CMFD, 36, PFUR, M., 2010, 87–111; Journal of Mathematical Sciences, 171:1 (2010), 89–115
\Bibitem{KorKonChe10}
\by V.~I.~Korzyuk, O.~A.~Konopel'ko, E.~S.~Cheb
\paper Boundary-value problems for fourth-order equations of hyperbolic and composite types
\inbook Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17--24, 2008). Part~2
\serial CMFD
\yr 2010
\vol 36
\pages 87--111
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd158}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2752652}
\transl
\jour Journal of Mathematical Sciences
\yr 2010
\vol 171
\issue 1
\pages 89--115
\crossref{https://doi.org/10.1007/s10958-010-0128-2}
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Linking options:
https://www.mathnet.ru/eng/cmfd158
https://www.mathnet.ru/eng/cmfd/v36/p87
This publication is cited in the following 3 articles:
V. I. Korzyuk, Ya. V. Rudko, “Klassicheskoe reshenie smeshannoi zadachi s usloviyami Dirikhle i Neimana dlya nelineinogo bivolnovogo uravneniya”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXV», Voronezh, 26-30 aprelya 2024 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 235, VINITI RAN, M., 2024, 40–56
V. I. Korzyuk, J. V. Rudzko, “Initial-boundary value problem with Dirichlet and Wentzell conditions for a mildly quasilinear biwave equation”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 166, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2024, 377–394
Victor Korzyuk, Nguyen Van Vinh, Nguyen Tuan Minh, “CLASSICAL SOLUTION OF THE CAUCHY PROBLEM FOR BIWAVE EQUATION: APPLICATION OF FOURIER TRANSFORM”, Mathematical Modelling and Analysis, 17:5 (2012), 630
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