Models of multiparameter bifurcations in boundary value problems for~ODEs of the fourth order on divergence of~elongated plate in~supersonic gas flow
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 2, pp. 24-35
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At the application of bifurcation theory methods to nonlinear boundary value problems for ordinary differential equations of the fourth and higher order there usually arise technical difficulties, connected with determination of bifurcation manifolds, spectral investigation of the direct and conjugate linearized problems and the proof of their Fredholm property. For overcoming of this difficulty here the roots separation method is applied to the relevant characteristic equations with subsequent presentation of critical manifolds, that allows to investigate nonlinear problems in the precise statement. Such approach is applied here to two-point boundary value problem for the nonlinear ODE of the fourth order describing the buckling (divergence) of an elongated plate in a supersonic flow of gas, subjected to compressed or extended boundary stresses at the various boundary fastenings.
Keywords:
buckling of an elongated plate; bifurcation; Fredholm property.
@article{VYURU_2015_8_2_a1,
author = {T. E. Badokina and B. V. Loginov},
title = {Models of multiparameter bifurcations in boundary value problems {for~ODEs} of the fourth order on divergence of~elongated plate in~supersonic gas flow},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
pages = {24--35},
publisher = {mathdoc},
volume = {8},
number = {2},
year = {2015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VYURU_2015_8_2_a1/}
}
TY - JOUR AU - T. E. Badokina AU - B. V. Loginov TI - Models of multiparameter bifurcations in boundary value problems for~ODEs of the fourth order on divergence of~elongated plate in~supersonic gas flow JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie PY - 2015 SP - 24 EP - 35 VL - 8 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VYURU_2015_8_2_a1/ LA - en ID - VYURU_2015_8_2_a1 ER -
%0 Journal Article %A T. E. Badokina %A B. V. Loginov %T Models of multiparameter bifurcations in boundary value problems for~ODEs of the fourth order on divergence of~elongated plate in~supersonic gas flow %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie %D 2015 %P 24-35 %V 8 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/VYURU_2015_8_2_a1/ %G en %F VYURU_2015_8_2_a1
T. E. Badokina; B. V. Loginov. Models of multiparameter bifurcations in boundary value problems for~ODEs of the fourth order on divergence of~elongated plate in~supersonic gas flow. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 2, pp. 24-35. http://geodesic.mathdoc.fr/item/VYURU_2015_8_2_a1/