| Article |
|---|
| Article name |
On the Solution of the Dirichlet Problem in the Half-Plane for Divergent Equations with Piecewise Smooth Coefficients |
| Authors |
Kholodovsky S.Y. Doctor of Physics and Mathematics, hol47@yandex.ru |
| Bibliographic description |
Kholodovskii S. Ye. On the Solution of the Dirichlet Problem in the Half-Plane for Divergent Equations with Piecewise Smooth Coefficients / / Scholarly Notes of Transbaikal State University. 2020. Vol. 15, No 3. PP. 38-45. DOI: 10.21209/2658-7114-2020-15-3-38-45. |
| Section |
PROBLEMS OF MATHEMATICAL PHYSICS. ANALYTICAL METHODS |
| UDK |
517.956 |
| DOI |
10.21209/2658-7114-2020-15-3-38-45 |
| Article type |
|
| Annotation |
The first boundary-value problem in a half-plane y < 0 consisting of two quadrants D1(x < 0)
and D2(x > 0), in which the divergence equation has coefficients of the form respectively,
k1(x) = a(b1x — 1)- 2 and k2(x) = a(b2x + 1)- 2, is considered. On the line x = 0 there
are conjugation conditions. This problem simulates the established processes of heat and mass
transfer in inhomogeneous media with a continuous permeability function that has a maximum
on the line x = 0. Bv the method of convolution of Fourier expansions, the solution of the
problem is expressed through the solution of the classical Dirichlet problem in the half-plane for
the Laplace equation.
|
| Key words |
boundary value problems, divergence equation, inhomogeneous permeable
media, generalized conjugation conditions, method of convolution of Fourier expansions |
| Article information |
|
| References |
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| Full article | On the Solution of the Dirichlet Problem in the Half-Plane for Divergent Equations with Piecewise Smooth Coefficients |
