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Existence and uniqueness theorem for solutions of dynamic problems of the nonlinear theory of elasticity. (English. Russian original) Zbl 0464.73019

J. Appl. Math. Mech. 44, 501-507 (1981); translation from Prikl. Mat. Mekh. 44, 710-719 (1980).

MSC:

74B20 Nonlinear elasticity
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
39B52 Functional equations for functions with more general domains and/or ranges
47B38 Linear operators on function spaces (general)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:

[1] Novozhilov, V. V., Foundations of the Nonlinear Theory of Elasticity (1952), Graylock Press: Graylock Press Rochester, New York, English translation
[2] Eringen, A. C., Nonlinear Theory of Continuous Media (1962), McGraw-Hill: McGraw-Hill New York
[3] Duvaut, G.; Lions, J.-L., Les Inéquations en Mécanique et en Physique (1972), Dunod: Dunod Paris · Zbl 0298.73001
[4] Vil’ke, V. G., Existence and uniqueness of solutions of certain classes of dynamic problems of nonlinear elasticity theory, PMM, Vol.43, No.1 (1979) · Zbl 0439.73016
[5] Besov, O. V.; Il’in, V. P.; Nikol’skii, S. M., Integral Representations of Functions and Embedding Theorems (1975), Nauka: Nauka Moscow · Zbl 0352.46023
[6] Pontryagin, L. S., Ordinary Differential Equations, (Book No. 09699 (1964), Pergamon Press), English translation · Zbl 0098.05502
[7] Tosida, K., Functional Analysis (1967), Mir: Mir Moscow
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