Abstract
In order to find approximate solutions to some continuum mechanics problems that admit variational statements, we use an approach that is based on restricting the class of functions in which we seek an extremal for the action functional. We demonstrate the method by some examples for the problem of forced oscillations of a nonlinear elastic membrane (in particular, a string), the problem of a fluid flow through a porous obstacle, and the problem of stationary waves on the surface of a heavy fluid.
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Original Russian Text © V.I. Nalimov, 2010, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2010, Vol. XIII, No. 2, pp. 111–123.
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Nalimov, V.I. Variational methods for constructing approximate solutions to some continuum mechanics problems. J. Appl. Ind. Math. 5, 259–270 (2011). https://doi.org/10.1134/S199047891102013X
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DOI: https://doi.org/10.1134/S199047891102013X