Representation theory for classes of initial value problems with quaternionic analysis

Abstract

AbstractWe consider time‐dependent Stokes problems for the case of low Reynolds number in smoothly bounded domains. By using a finite difference time discretization, the problem is reduced to a sequence of steady‐state Stokes problems. These boundary value problems are solved by means of hypercomplex analysis. In the second part, we consider initial boundary value problems of the so‐called Galpern–Sobolev type. An implicit time discretization method is deduced. Making use of a modified Teodorescu transform and suitable quaternionic Hilbert space projections, we obtain a representation of the solution. Copyright © 2002 John Wiley & Sons, Ltd.