On the Boundary Value Problem in A Dihedral Angle for Normally Hyperbolic Systems of First Order

1998 ◽  
Vol 5 (2) ◽  
pp. 121-138
Author(s):  
O. Jokhadze
Keyword(s):  
Partial Differential Equations ◽  
Boundary Value Problem ◽  
Principal Part ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Order System ◽  
First Order ◽  
Dimensional Boundary ◽  
Class Of Functions

Abstract Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.

The Three-Dimensional Problem of Statics of the Elastic Mixture Theory with Displacements Given on the Boundary

1999 ◽  
Vol 6 (6) ◽  
pp. 517-524
Author(s):  
M. Basheleishvili
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Three Dimensional ◽  
Mixture Theory ◽  
Potential Method ◽  
Fredholm Integral Equations ◽  
Infinite Domains ◽  
Elastic Mixture ◽  
Uniqueness Of The Solution ◽  
Dimensional Boundary

Abstract The first three-dimensional boundary value problem is considered for the basic equations of statics of the elastic mixture theory in the finite and infinite domains bounded by the closed surfaces. It is proved that this problem splits into two problems whose investigation is reduced to the first boundary value problem for an elliptic equation which structurally coincides with an equation of statics of an isotropic elastic body. Using the potential method and the theory of Fredholm integral equations of second kind, the existence and uniqueness of the solution of the first boundary value problem is proved for the split equation.

Lifting three-dimensional wings in transonic flow

1979 ◽  
Vol 95 (2) ◽  
pp. 223-240 ◽  
Author(s):  
M. S. Cramer
Keyword(s):  
Boundary Value Problem ◽  
Asymptotic Expansions ◽  
Transonic Flow ◽  
Near Field ◽  
Boundary Value ◽  
Three Dimensional ◽  
Matched Asymptotic Expansions ◽  
Far Field ◽  
First Order ◽  
Order Contribution

The far field of a lifting three-dimensional wing in transonic flow is analysed. The boundary-value problem governing the flow far from the wing is derived by the method of matched asymptotic expansions. The main result is to show that corrections which are second order in the near field make a first-order contribution to the far field. The present study corrects and simplifies the work of Cheng & Hafez (1975) and Barnwell (1975).

A note on ‘Lifting three-dimensional wings in transonic flow’ by M. S. Cramer

1981 ◽  
Vol 109 ◽  
pp. 257-258 ◽  
Author(s):  
M. S. Cramer
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Transonic Flow ◽  
Boundary Value ◽  
Three Dimensional ◽  
Far Field ◽  
First Order ◽  
Order Of Magnitude

The purpose of this note is to clarify the discrepancy between the results of Cramer (1979), Barnwell (1975) and Cheng & Hafez (1975). These authors have all derived the boundary-value problem governing the flow far from a three-dimensional lifting wing in transonic flow. The results of both Cramer and Barnwell will provide the lowest-order solution in the far field. The results of Cheng & Hafez are not only accurate to lowest order but to first order as well. That is, the theory of Cheng & Hafez is an order-of-magnitude more accurate than those of Barnwell and Cramer. This is the reason for the discrepancy between the boundary condition derived by Cheng & Hafez and that of Cramer and Barnwell. Because Cheng & Hafez correctly derive the first-order results, the lowest-order theories of Cramer or Barnwell cannot correct those of Cheng & Hafez. It should be recognized that the main contribution of Cramer's work was to clarify the structure of the problem and to simplify the analysis rather than correct the basic results.

Sign in / Sign up

Export Citation Format

Share Document