Open AccessOn one approach to the solution of miscellaneous problems of the theory of elasticity
Author(s) -
В. В. Амелькин,
М. Н. Василевич,
L. A. Khvostchinskaya
Publication year - 2021
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2021-57-3-263-273
Subject(s) - mathematics , mathematical analysis , logarithm , piecewise , boundary value problem , elasticity (physics) , riemann problem , complex plane , singular solution , riemann hypothesis , physics , thermodynamics
Herein, a miscellaneous contact problem of the theory of elasticity in the upper half-plane is considered. The boundary is a real semi-axis separated into four parts, on each of which the boundary conditions are set for the real or imaginary part of two desired analytical functions. Using new unknown functions, the problem is reduced to an inhomogeneous Riemann boundary value problem with a piecewise constant 2 × 2 matrix and four singular points. A dierential equation of the Fuchs class with four singular points is constructed, the residue matrices of which are found by the logarithm method of the product of matrices. The single solution of the problem is represented in terms of Cauchy-type integrals when the solvability condition is met.