Lobachevskii Journal of Mathematics
Volume I
Contents

Title:

On geometrical properties of free boundaries in the HeleShaw flows moving
boundary problem

Author: Yu.E. Hohlov

Address: Institute of Applied Mathematics of Russian Academy
of Sciences, Moscow, Russia

email: hohlov@math.ru

Author: D.V. Prokhorov

Address: Department of Mathematics and Mechanics Saratov State
University Saratov

email: prokhor@scnit.saratov.su

Author: A.Ju. Vasil'ev

Address: Departamento de Matematicas Universidad de Los Andes
Santafe de Bogota, Colombia

email: avassill@uniandes.edu.co

Abstract:

In the article we discuss the geometrical properties of the moving boundary
for two basic cases in the plain problem of the HeleShaw flows: for the
inner problem for the flows in a bounded simply connected domain; and for
the exterior problem for dynamics of an aerofoil connected with the flows
in the exterior part of a bounded simply connected domain. We prove the
invariance of the properties of starlikeness in case of the inner problem
of pumping; of convexity in case of the exterior problem of tightening
of an aerofoil. We also adduce some examples for the problem of tightening
where the corresponding properties of starlikeness, convexity and closetoconvexity
are not inherited by the moving boundary.

Source: DVI format (50Kb), ZIPed PostScript
format(54Kb),


Title:

ABSOLUTELY CONVERGENT DIRICHLET SERIES AND ANALYTIC CONTINUATION OF ITS
SUM

Author: Yu. F. Korobeinik

Address: Faculty of Mechanics and Mathematics
Rostov State University
5 Zorge st., Rostov~on~Don
344090 Russia
email: kor@mmf.unird.ac.ru

Abstract:

The paper contains some results on analytic continuation of the sum of
Dirichlet series obtained with the help of the wellknown Ploya theorem.
A special attention is paid to an effective determination of the domain
into which the sum of series can be continued analytically. Some methods
of the effective continuation of the sum of Dirichelt series are considered
including, in particular, the analytic continuation by means of initial
series. In this part of paper the author employs the results of Leont'ev
and other russian mathematicians including his own. A many dimensional
analogue of Polya theorem is also obtained as well as some results on analytic
continuation of its sum. Finally, the characterization of the exact domain
of absolute convergence of manydimensional Dirichlet series is given under
comparatively mild restriction.
Source: DVI format (162Kb), ZIPed PostScript
format(118Kb), ZIPed DVI format (62Kb)
Back to LJM homepage
