Geodesic
On the stability of solutions of certain classes of initial-boundary-value problems in aerohydroelasticity
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 34-46

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We study the stability of solutions to initial–boundary-value problems for coupled systems of partial differential equations describing the dynamics of deformable structural elements interacting with a gas-liquid medium. The definitions of stability of deformable bodied adopted in this work correspond to the concept of the Lyapunov stability of dynamic systems. The stability of deformable elements of vibration devices interacting with subsonic and supersonic flows is examined. The effect of a gas or liquid (in the model of an ideal compressible medium) is determined from asymptotic equations of aerohydromechanics. For the description of the dynamics of elastic elements, we use nonlinear models of solid deformable bodies with transverse and longitudinal deformations. Models are described by coupled nonlinear systems of partial differential equations. The study of stability is based on the construction of positive-definite Lyapunov-type functionals corresponding to these systems; sufficient conditions for the stability of their solutions are obtained.
Keywords: aerohydroelasticity, mathematical modeling, dynamic stability, elastic plate, subsonic flow, supersonic flow, partial differential equation, functional. 
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     author = {P. A. Vel'misov and A. V. Ankilov and Yu. V. Pokladova},
     title = {On the stability of solutions of certain classes of initial-boundary-value problems in aerohydroelasticity},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {34--46},
     publisher = {mathdoc},
     volume = {165},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_165_a3/}
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P. A. Vel'misov; A. V. Ankilov; Yu. V. Pokladova. On the stability of solutions of certain classes of initial-boundary-value problems in aerohydroelasticity. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 34-46. http://geodesic.mathdoc.fr/item/INTO_2019_165_a3/