On the Existence of a Solution of Point Source Blast Wave Equation

DOI
  • SAKURAI A.
    Department of Mathematical Science, School of Science and Engineering, Tokyo Denki University
  • ARAI T.
    Department of Mathematical Science, School of Science and Engineering, Tokyo Denki University

Bibliographic Information

Other Title
  • 爆風方程式の解の存在

Abstract

It is noted that the use of blast effects in actual engineering applications requires an accurate prediction. The existence of a solution of the basic point-source blast wave equation is considered in this connection. Among many existing approximate solutions, a particular attention is paid to the solution in the form of power series expansion in y, where y=C2/U2, U is the front shock speed and C the sound velocity. It is proved that the above series expansion, in fact, converges for y ≤ y for a certain small y, and is a solution of the system of equations obtained by the blast wave transformation of the original equations of motion for the point-source blast wave.<BR>Acutual process of the proof is in the following manner : First, a Banach space is introduced, which consists of functions expressed in the form of convergent series expansion in y. Next, the above system of equations is converted into the one which determines a fixed point of a mapping in this space. The mapping is then shown to have the property of contraction in closed ball in the space if y≤y. The existence of a fixed point in the ball, hence the existence of the solution of the original system for y≤y, follows immediately.

Journal

Keywords

Details 詳細情報について

  • CRID
    1390282679672300928
  • NII Article ID
    130004005356
  • DOI
    10.11426/nagare1982.1.80
  • ISSN
    21854912
    02863154
  • Text Lang
    ja
  • Data Source
    • JaLC
    • CiNii Articles
  • Abstract License Flag
    Disallowed

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