Geodesic
Nonlinear panel flutter. Bolotin's problem in the presence of viscous friction
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2, Tome 186 (2020), pp. 45-51

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In this paper, we consider a nonlinear boundary-value problem proposed as the simplest model for describing oscillations in a gas flow. We analyze the stability of the zero equilibrium state and find a critical value of the velocity of the incoming gas flow. Exact solutions of the problem are found in the form of time-periodic functions and their stability is examined. All the results are obtained analytically based on the qualitative theory of infinite-dimensional dynamical systems.
Keywords: nonlinear boundary-value problem, theory of aeroelasticity, stability, periodic solution, panel flutter. 
@article{INTO_2020_186_a5,
     author = {A. S. Zapov},
     title = {Nonlinear panel flutter. {Bolotin's} problem in the presence of viscous friction},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {45--51},
     publisher = {mathdoc},
     volume = {186},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_186_a5/}
}
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A. S. Zapov. Nonlinear panel flutter. Bolotin's problem in the presence of viscous friction. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2, Tome 186 (2020), pp. 45-51. http://geodesic.mathdoc.fr/item/INTO_2020_186_a5/