Solving spectral problems in piecewise homogeneous media

1995 ◽  
Vol 75 (4) ◽  
pp. 1866-1871
Author(s):  
V. G. Prikazchikov ◽  
A. S. Medvedyev
Keyword(s):  
Spectral Problems ◽  
Piecewise Homogeneous Media ◽  
Homogeneous Media

scholarly journals Matrix Fourier Transforms for Consistent Mathematical Models

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Oleg Yaremko ◽  
Natalia Yaremko
Keyword(s):  
Mathematical Models ◽  
Fourier Transforms ◽  
Integral Form ◽  
Integral Transforms ◽  
Mathematical Physics ◽  
Discontinuous Coefficients ◽  
Piecewise Homogeneous Media ◽  
Fourier Matrix ◽  
Matrix Transforms ◽  
Homogeneous Media

We create a matrix integral transforms method; it allows us to describe analytically the consistent mathematical models. An explicit constructions for direct and inverse Fourier matrix transforms with discontinuous coefficients are established. We introduce special types of Fourier matrix transforms: matrix cosine transforms, matrix sine transforms, and matrix transforms with piecewise trigonometric kernels. The integral transforms of such kinds are used for problems solving of mathematical physics in homogeneous and piecewise homogeneous media. Analytical solution of iterated heat conduction equation is obtained. Stress produced in the elastic semi-infinite solid by pressure is obtained in the integral form.

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