Lobachevskii Journal of Mathematics

Volume I

      On geometrical properties of free boundaries in the Hele-Shaw flows moving boundary problem
      Author: Yu.E. Hohlov
      Address: Institute of Applied Mathematics of Russian Academy

      of Sciences, Moscow, Russia
      e-mail: hohlov@math.ru
      Author: D.V. Prokhorov
      Address: Department of Mathematics and Mechanics Saratov State

      University Saratov
      e-mail: prokhor@scnit.saratov.su
      Author: A.Ju. Vasil'ev
      Address: Departamento de Matematicas Universidad de Los Andes

      Santafe de Bogota, Colombia
      e-mail: avassill@uniandes.edu.co
      In the article we discuss the geometrical properties of the moving boundary for two basic cases in the plain problem of the Hele-Shaw 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 close-to-convexity are not inherited by the moving boundary.
      Source: DVI format (50Kb), ZIP-ed PostScript format(54Kb),

    Author: Yu. F. Korobeinik
    Address: Faculty of Mechanics and Mathematics

    Rostov State University
    5 Zorge st., Rostov~on~Don
    344090 Russia
    e-mail: kor@mmf.unird.ac.ru
    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 many-dimensional Dirichlet series is given under comparatively mild restriction.
    Source: DVI format (162Kb), ZIP-ed PostScript format(118Kb), ZIP-ed DVI format (62Kb)

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