On a nonlocal boundary value problem for a system of singular differential equations

Abstract

This article deals with a system consisting of singular partial differential equations of the first and second order arising in the zero approximation of I. Vekua's hierarchical models of prismatic shells, when the thickness of the shell varies as a power function of one argument and vanishes at the cusped edge of the shell. For this system of special type a nonlocal boundary value problem in a half-plane is solved in the explicit form. The boundary value problem under consideration corresponds to stress–strain state of the cusped prismatic shell under the action of concentrated forces and moments.

Keywords:

• Systems of special type
• Systems of singular partial differential equations
• Degenerate elliptic equations
• Cusped prismatic shells
• Cusped plates

Mathematics Subject Classification (2000): :

• 35M99
• 35J70
• 74K20
• 74K25

Acknowledgement

This work is partly supported by INTAS Project 06-100017-8886.