Kuksin, S. B. An averaging theorem for distributed conservative systems and its application to von Kármán’s equations. (English. Russian original) Zbl 0722.73039 J. Appl. Math. Mech. 53, No. 2, 150-157 (1989); translation from Prikl. Mat. Mekh. 53, No. 2, 196-205 (1989). Summary: An averaging theorem, of the Krylov-Bogolyubov-Mitropols’kij type, is proved for oscillatory processes in spatially-multidimensional conservative systems. Von Kármán’s equations are considered as an example. Cited in 2 Documents MSC: 74H45 Vibrations in dynamical problems in solid mechanics 74K20 Plates 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 34C29 Averaging method for ordinary differential equations Keywords:Krylov-Bogolyubov-Mitropols’kij type; oscillatory processes; spatially- multidimensional conservative systems PDFBibTeX XMLCite \textit{S. B. Kuksin}, J. Appl. Math. Mech. 53, No. 2, 150--157 (1989; Zbl 0722.73039); translation from Prikl. Mat. Mekh. 53, No. 2, 196--205 (1989) Full Text: DOI References: [1] Zakharov, V. E., Hamiltonian formalism for waves in non-linear media with dispersion, Izv. Vuz. Radiofizika, 17, 4 (1974) [2] Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P., Integrable systems, (Fundamental Trends. Fundamental Trends, Itogi Nauki i Tekhniki Ser. Sovr. Probl. Matematiki, 4 (1985), VINITI: VINITI Moscow) · Zbl 0780.58019 [3] Chernoff, P. R.; Marsden, J. E., Properties of Infinite Dimensional Hamiltonian Systems (1974), Springer: Springer Berlin · Zbl 0328.58009 [4] Arnol’d, V. I., Mathematical Methods of Classical Mechanics (1974), Nauka: Nauka Moscow · Zbl 0647.70001 [5] Berdichevskii, V. L., Variational Principles of the Mechanics of Continuous Media (1983), Nauka: Nauka Moscow · Zbl 0158.46505 [6] Bogolyubov, N. N.; Mitropol’skii, Yu. A., Asymptotic Methods in the Theory of Non-linear Oscillations (1958), Fizmatgiz: Fizmatgiz Moscow · Zbl 0083.08101 [7] Kalyakin, L. A., Long-wave asymptotic forms of the solution of a hyperbolic system of equations, Mat. Sbornik, 124, 1 (1984) · Zbl 0566.35066 [8] Ostrovskii, L. A., Approximate methods in the theory of non-linear waves, Izv. Vuz. Radiofizika, 17, 4 (1974) · Zbl 0292.35056 [9] Dobrokhotov, S. Yu.; Maslov, V. P., Multiphase asymptotics of non-linear partial differential equations with a small parameter, Soviet Sci. Revs., Sec. C. Math., Phys. Revs., 3 (1982) · Zbl 0551.35072 [10] Karasev, M. V.; Maslov, V. P., Asymptotic and geometric quantization, Uspekhi. Mat. Nauk, 39, 6 (1984) · Zbl 0588.58031 [11] Lions, J.-L., Quelques méthodes de résolution des problémes aux limites non linéaires (1969), Dunod: Dunod Paris · Zbl 0189.40603 [12] Ciarlet, P. G.; Rabier, P., Les équations de von Kármán (1980), Springer: Springer Berlin · Zbl 0433.73019 [13] Kuksin, S. B., Hamiltonian perturbations of infinite-dimensional linear systems with imaginary spectrum, Funkts. Anal. Prilozhen., 21, 3 (1987) · Zbl 0631.34069 [14] Arnol’d, V. I., Proof of a theorem of A.N. Kolmogorov on the conservation of conditionally periodic motions under a small change in the Hamiltonian function, Uspekhi Mat. Nauk, 18, 5 (1963) [15] Brezis, H., Opérateurs maximaux monotones et sémigroupes de contractions dans les espaces de Hilbert (1973), North-Holland: North-Holland Amsterdam-London · Zbl 0252.47055 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.