TY - JOUR
AU - I. O. Lukovsky
PY - 2018/01/25
Y2 - 2020/11/28
TI - Variational method for the solution of nonlinear boundary-value problems of the
dynamics of bounded volumes of liquid with variable boundaries
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 70
IS - 1
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1542
AB - We study nonlinear boundary-value problems of the hydrodynamic type formulated for the domains whose boundariesare unknown in advance. The investigations are based on the variational formulations of these problems with the help ofspecially introduced integral functionals with variable domains of integration. It is shown that the required solutions of theboundary-value problems are, in a certain sense, equivalent to finding stationary points of the analyzed functionals. Theseare pairs formed by the families of domains and the functions defined in these domains. On an example of the problem ofspace motion of a vessel with elastic walls partially filled with an ideal incompressible liquid, we propose a method for theconstruction in the analytic form both of the required solutions and of the boundaries of the domains (deformed walls andthe shape of the perturbed free surface of the liquid).
ER -