| Article |
|---|
| Article name |
Dirichlet Problem in a Strip for Divergent Equations with Monotone Discontinuous Coefficients. Cases of the Solution to the Problem in the Final Form |
| Authors |
Kholodovsky S.Y. Doctor of Physics and Mathematics, hol47@yandex.ruYefimova I.A. Candidate of Physics and Mathematics, hol47@yandex.ru |
| Bibliographic description |
Kholodovskii S. Ye., Efimova I. A. On the Solution of the Dirichlet Problem in the HalfPlane for Divergent Equations with Piecewise Smooth Coefficients. Cases of the Solution to the Problem in the Final Form / / Scholarly Notes of Transbaikal State University. 2020. Vol. 15, No 3. PP. 46-51. DOI: 10.21209/2658-7114-2020-15-3-46-51. |
| Section |
PROBLEMS OF MATHEMATICAL PHYSICS. ANALYTICAL METHODS |
| UDK |
517.956 |
| DOI |
10.21209/2658-7114-2020-15-3-46-51 |
| Article type |
|
| Annotation |
The first boundary-value problem is considered in a strip - l < x < l , y £ R consisting of
two inhomogeneous zones D1( - l < x < 0) and D2(0 < x < l) in which the divergence equation
has coefficients of the form K 1(x) = k1(b1x + 1)2 and K2(x) = k2(b2x + 1)2, respectively, where
the constants kj, b satisfy the condition k1b1 = k2b2. The solution to the problem is expressed in
its final form through the solution of the classical Dirichlet problem in the strip for the Laplace
equation.
|
| Key words |
boundary value problems in a strip, divergence equation, piecewise-continuous
permeability functions, conjugation conditions |
| Article information |
|
| References |
1. Dombrovskij, G. А. О nekotorvh sistemah uravnenij s chastnvmi proizvodnvmi
pervogo porvadka i sootvetstvuvushchih obobshchennvh uravnenivah Ejlera-Puassona-Darbu / /
Differencial’nye uravneniva. 1978. T. 14. № 1. S. 121-124.
2. CHernvaev, A. P. Postroenie osnovnvh reshenij obobshchennoj sistemv Koshi-Rimana
pervogo porvadka s koefficientom, zavisvashchim ot odnoj peremennoj po gipertangensaknomu
zakonu / / Differencial’nye uravneniva. 1981. T. 17. № 11. S. 2071-2083.
3. Polozhij, G. I. Obobshchenie teorii analiticheskih funkcij kompleksnogo peremennogo.
Kiev: Izd-vo Kievskogo un-ta, 1965. 442 c.
4. Holodovskij, S. E. Metod svertvvaniva razlozhenij Fur’e. Sluchaj treshchinv (zavesv) v
neodnorodnom prostranstve / / Differencial’nve uravneniva. 2009. T. 45. № 8. S. 1204-1208. |
| Full article | Dirichlet Problem in a Strip for Divergent Equations with Monotone Discontinuous Coefficients. Cases of the Solution to the Problem in the Final Form |
