Accession Number:

AD0733497

Title:

Similarity Solutions for Partial Differential Equations Generated by Finite and Infinitesimal Groups,

Descriptive Note:

Corporate Author:

IOWA INST OF HYDRAULIC RESEARCH IOWA CITY

Personal Author(s):

Report Date:

1971-07-01

Pagination or Media Count:

101.0

Abstract:

The problem of developing systematic methods for obtaining similarity variables is considered for partial differential equations. Similarity variables are a set of transformations which reduce a partial differential equation to an ordinary differential equation. This paper considers two methods of generating similarity variables. The first method uses a group of finite transformations and the second uses a group of infinitesimal transformations. The mathematical theory for both techniques is described and illustrated. The two methods of obtaining similarity variables are applied to the Burgers equation usub y uu sub x u sub xx and to the laminar boundary layer equations with a pressure gradient. In all cases considered, new types of similarity variables are found. In addition, the auxiliary conditions are discussed in the light of the new similarity variables obtained for the boundary layer equations. Author

Subject Categories:

  • Theoretical Mathematics
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE