scholarly journals The spectral function of a first order elliptic system

2013 ◽  
Vol 3 (3) ◽  
pp. 317-360 ◽  
Author(s):  
Olga Chervova ◽  
Robert Downes ◽  
Dmitri Vassiliev
Keyword(s):  
Spectral Function ◽  
Elliptic System ◽  
First Order ◽  
Order Elliptic System

A first-order elliptic system with semiregular degeneracy

1988 ◽  
Vol 28 (4) ◽  
pp. 327-331
Author(s):  
A. Gedvilaitė ◽  
L. Kaklauskas ◽  
D. Jurgaitis
Keyword(s):  
Elliptic System ◽  
First Order ◽  
Order Elliptic System

On the Dirichlet Problem for a Second Order Elliptic System with Degeneration on the Entire Domain Boundary

1999 ◽  
Vol 6 (4) ◽  
pp. 395-400
Author(s):  
M. Usanetashvili
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Elliptic System ◽  
Domain Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Entire Domain ◽  
Order Elliptic System

Abstract The solvability of the first boundary value problem is investigated for a second order elliptic system with degeneration on the entire domain boundary.

Elastodynamic Local Fields for a Crack Running in an Orthotopic Medium

1991 ◽  
Vol 58 (4) ◽  
pp. 982-987 ◽  
Author(s):  
A. Piva ◽  
E. Radi
Keyword(s):  
Dynamic Stress ◽  
Equations Of Motion ◽  
Local Fields ◽  
Stress Fields ◽  
Orthotropic Materials ◽  
Displacement Fields ◽  
First Order ◽  
Stress And Displacement Fields ◽  
Order Elliptic System ◽  
Separated Variables

The dynamic stress and displacement fields in the neighborhood of the tip of a crack propagating in an orthotropic medium are obtained. The approach deals with the methods of linear algebra to transform the equations of motion into a first-order elliptic system whose solution is sought under the assumption that the local displacement field may be represented under a scheme of separated variables. The analytical approach has enabled the distinction between two kinds of orthotropic materials for which explicit espressions of the near-tip stress fields are obtained. Some results are presented graphically also in order to compare them with the numerical solution given in a quoted reference.

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