Geodesic
Boundary-value problems for fourth-order equations of hyperbolic and composite types
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, Tome 36 (2010), pp. 87-111

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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. 
@article{CMFD_2010_36_a7,
     author = {V. I. Korzyuk and O. A. Konopel'ko and E. S. Cheb},
     title = {Boundary-value problems for fourth-order equations of hyperbolic and composite types},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {87--111},
     publisher = {mathdoc},
     volume = {36},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2010_36_a7/}
}
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V. I. Korzyuk; O. A. Konopel'ko; E. S. Cheb. Boundary-value problems for fourth-order equations of hyperbolic and composite types. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, Tome 36 (2010), pp. 87-111. http://geodesic.mathdoc.fr/item/CMFD_2010_36_a7/