Вариационные формулировки нелинейных краевых задач со свободной границей теории взаимодействия поверхностных волн с акустическими полями

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.