of free fall, Ix[ 2 = x~ + x~, and v0 is the unique positive root ... The method of integral equations has not been studied as well for problem (1.2)-(1.6). We briefly ...
INTEGRAL EQUATIONS FOR THE PROBLEM OF STATIONARY WAVES PRODUCED BY A FLOATING BODY N. G. Kuznetsov
I,
Suppose that an ideal incompressible heavy fluid fills a region
(x, y): y < 0 ,
x = (xl,x2)~R~}.
the following non-intersecting i)
W CR[
If its depth is infinite then the boundary
= {P =
0Wconsists
of
sets.
The moistened surface S of a body that is partially submerged in the fluid and
that fills a bounded simply connected region D in R ~ such that D ~ OR[ nected two-dimensional region. 2)
The free fluid surface
3)
The bottom
is a simply con-
Here S = OD N R~. F = aR[ ~ D.
B = {PER[:
y = --h}, where h > 0.
In the case of infinite depth we can assume that h = ~. We assume that the surface 8D belongs to the class C 2 and for every point of P contained in the water line
OR[.
the tangent surface to 3D is not equal to 3R~.
Then
O 0 the potential Vu has a finite Dirichlet integral over a cylindrical region {Ix l
