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Volume 18,     Number 4,     Winter 2010

 

A SYMMETRY APPROACH TO AN INITIAL
MOVING BOUNDARY VALUE PROBLEM
ASSOCIATED WITH THE WAVE EQUATION
NORMAN C. CORBETT

Abstract. A number of studies involving tethered space craft have led to an interest in hyperbolic equations that are defined on time dependent domains. In the case of the one-dimensional wave equation with a general moving endpoint x = s(t), it appears that Moore (see [10]) was the first to find a formal series solution. However, an alternative derivation, based on the point symmetries of the wave equation, remains unknown. In this paper we outline this derivation and show how the Lie group of point transformations, admitted by the one-dimensional wave equation, can be used to find a general series solution for an associated initial moving boundary value problem.

 

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