# Accession Number:

## AD0272186

# Title:

## ON PERTURBATIONS OF SIMILARITY SOLUTIONS

# Descriptive Note:

# Corporate Author:

## AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO

# Personal Author(s):

# Report Date:

## 1961-12-01

# Pagination or Media Count:

## 1.0

# Abstract:

An inhomogeneous boundary value problem for the whole strip extending from negative to positive infinity is presented. Then a two-sided Laplace transformation is applied. The transform is defined by an inhomogeneous ordinary differential equation. In part of the plane of the Laplace transform the s-plane a boundary condition for the boundary in the original plane that is the characteristic, is obtained by the requirement that the Laplace transform must be bounded at this point. In the remainder of the s-plane the Laplace transform is defined by analytical continuation. The poles and the residues at the poles can be characterized in rather general terms by the properties of the homogeneous solutions of the equation for the Laplace transform. The solution in the original plane can then be expressed by means of the inversion integral. One then proceeds to express the solution in terms of the residues at the poles. This is equivalent to representation by means of a superposition of the particular solutions mentioned above. To obtain such a representation a deformation of the path of integration in the complex s-plane is needed. To justify such a deformation one must study the behavior of the Laplace transform at infinity of the s-plane. Here the asymptotic theory for ordinary differential equations in the form developed by Langer and others is applied. Author