2017
Том 69
№ 9

All Issues

Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields

Lukovsky I. O., Timokha A. N.

Full text (.pdf)


Abstract

Variational problems equivalent to nonlinear evolutionary boundary-value problems with a free boundary are formulated. These problems arise in the theory of interaction of limited volumes of liquid, gas, and their interface with acoustic fields. It is proved that the principle of separation of motions can be applied to these variational problems. The problem of a capillary-acoustic equilibrium form is given in a variational formulation.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 12, pp 1849-1860.

Citation Example: Lukovsky I. O., Timokha A. N. Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields // Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1642–1652.

Full text