Geodesic
On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 110-116 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a model case of stationary vibrations of a thin flat plate, one side of which is embedded, the opposite side is free, and the sides are freely leaned. In mathematical modeling there is a local boundary value problem for the biharmonic equation in a rectangular domain. Boundary conditions are given on all boundary of the domain. We show that the considered problem is self-adjoint. Herewith the problem is ill-posed. We show that the stability of solution to the problem is disturbed. Necessary and sufficient conditions of existence of the problem solution are found. Spaces of the ill-posedness of the considered problem are constructed.
Keywords: oscillations; thin flat plate; biharmonic equation; boundary value problem; ill-posed problem. 
@article{VYURU_2016_9_2_a9,
     author = {U. A. Iskakova},
     title = {On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {110--116},
     year = {2016},
     volume = {9},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a9/}
}
TY  - JOUR
AU  - U. A. Iskakova
TI  - On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2016
SP  - 110
EP  - 116
VL  - 9
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a9/
LA  - en
ID  - VYURU_2016_9_2_a9
ER  - 
%0 Journal Article
%A U. A. Iskakova
%T On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2016
%P 110-116
%V 9
%N 2
%U http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a9/
%G en
%F VYURU_2016_9_2_a9
U. A. Iskakova. On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 110-116. http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a9/

[1] Kabanikhin S.I., “Inverse and Ill-Posed Problems”, Siberian Electronic Mathematical Reports, 7 (2010), 380–394

[2] Komkov V., Optimal Control Theory for the Damping of Vibrations of Simple Elastic Systems, Springer, Berlin–Heidelberg, 1972 | MR | Zbl

[3] Hadamard J., Le probleme de Cauchy et les equations aux derivees partialles lineaires hyperboliques, Hermann and Lie, Paris, 1932

[4] Lavrent'ev M.M., “On the Cauchy Problem for Laplace Equation”, Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 20:6 (1956), 819–842 (in Russian) | MR | Zbl

[5] Tikhonov A.N., “Non-linear Equations of First Kind”, Doklady akademii nauk SSSR, 161:5 (1965), 1023–1026 (in Russian) | MR | Zbl

[6] Kal'menov T.Sh., Iskakova U.A., “Criterion for the Strong Solvability of the Mixed Cauchy Problem for the Laplace Equation”, Doklady Mathematics, 75:3 (2007), 370–373 | DOI | MR | Zbl

[7] Kal'menov T.Sh., Iskakova U.A., “A Method for Solving the Cauchy Problem for the Laplace Equation”, Doklady Mathematics, 78:3 (2008), 874–876 | DOI | MR | Zbl

[8] Kal'menov T.Sh., Iskakova U.A., “On a Boundary Value Problem for the Biharmonic Equation”, AIP Conference Proceedings, 1676, 2015, 020031 | DOI