Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University20839Research ArticleStability of solution of one nonlinear initial-boundary problem of aeroelasticityAnkilovAndrey V(Ph. D. (Phys. & Math.)), Doctoral Candidate, Dept. of Higher Mathematics. Petrankil@ulstu.ruVel’misovA Aleksandrovich(Dr. Sci. (Phys. & Math.)), Professor, Dept. of Higher Mathematicsvelmisov@ulstu.ruKazakovaYulia A10 A, Krymov st., Ulyanovsk, 432071, Russiakazakova_ua@mail.ruUlyanovsk State Technical UniversityUlyanovsk Instrument Manufacturing Design Bureau1506201317212012618022020Copyright © 2013, Samara State Technical University2013The dynamic stability of an elastic element of the channel wall under the subsonic stream of an ideal compressible fluid (gas) is studied. Determination of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. The sufficient conditions for stability are obtained. Conditions impose limitations on the speed of the uniform stream of gas, compressed (tensile) element of efforts, the elastic element stiffness and other parameters of the mechanical system.aerohydroelasticitystabilityelastic platedeformationsubsonic flowcompressed liquid (gas)аэрогидроупругостьустойчивостьупругая пластинадеформациядозвуковой потоксжимаемая среда[Анкилов А. В., Вельмисов П. А. Устойчивость вязкоупругих элементов стенок проточных каналов. Ульяновск: Ульяновский гос. технич. ун-т, 2000. 115 с.][Коллатц Л. Задачи на собственные значения. М.: Наука, 1968. 503 с.]