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Scientific Bulletin of Namangan State University

Abstract

In this paper, we study a nonlocal boundary value problem with the Poincare condition for an equation of elliptic - hyperbolic type of the second kind, i.e. for the equation where the line of degeneracy is the characteristic. Due to the mathematical content and the presence of numerous applications in the study of problems in mechanics, physics, technology [1] and biology, the study of boundary value problems for degenerate elliptic equations and equations o f mixed type is in the focus o f specialists in partial differential equations. Further, it was found that nonlocal boundary conditions arise in the problems of predicting soil moisture [2], when modeling liquid filtration in porous media [3], in mathematical modeling of laser radiation processes and problems o f plasma physics [4], as well as in questions o f mathematical biology [5].

First Page

9

Last Page

14

References

1. Islomov V. I., Abdullayev A. A. On a problem for an elliptic type equation of the second kind with a conormal and integral condition. Nanosystems: Physics, Chemistry, Mathematics, 2018, 9 (3), P. 307-318 DOI 10.17586/22208054201893307318 2. Naxushev A.M. Ob odnom priblijennom metode resheniya krayevix zadach dlya differensialnix uravneniy i yego prilojeniya k dinamike pochvennoy vlagi i gruntovix vod. // «Differensialnie uravneniya». 1982. T.18. № 1. S.72-81. 3. Shxanukov M.X. O nekotorix krayevix zadachax dlya uravneniya tretego poryadka, voznikayushix pri modelirovanii filtratsii jidkosti v poristix sredax. // «Differensialnie uravneniya». 1982. T.XVIII. № 4. S.689-699. 4. Bassanini P., Calaverni M. Contrazioni multi sistemi iperbolici, eprobemia del laser // Atti Semin, mat. e. fis. Univ. Madena. 1982. Vol. 31. №1. P.32-50 5. M.C. Salaxitdinov, A.A. Abdullayev O yedinstvennosti resheniya zadachi dlya odnogo uravneniya tretego poryadka smeshannogo tipa vtorogo roda// .Dokladi Adigskoy (Cherkesskoy) Mejdunarodnoy Akademii Nauk ISSN: 1726-9946 T: 13 №: 2, 2011g. S. 9- 11 6. A.A. Abdullayev, N.M. Safarbayeva Ob odnoy krayevoy zadache dlya uravneniya smeshannogo tipa vtorogo roda // Vestnik NTU "XPI". Seriya: Informatika i modelirovaniye, 2018. - № 42 (1318). - S. 5-11. 7. A.A. Abdullayev. On the uniqueness of one boundary value problem for the ellipticohvperbolic equation of the second kind. Scientific Bulletin of Namangan State University 1 (8), 3-9 (2019) 8. A.A. Abdullayev O yedinstvennosti resheniya zadachi tipa Franklya dlya uravneniya elliptiko- giperbolicheskogo tipa vtorogo roda // Vestnik NTU "XPI". Seriya: Informatika i modelirovaniye. 2019. - № 13 (1338). -S . 5 - 12. 9. A.A. Abdullayev On uniqueness of a boundary value problem for an equation of elliptichvperbolic type of the second kind. Bulletin of the Institute of Mathematics (5), 30- 35 p. 2018. 10. A.A. Abdullayev, T.G. Ergashev. Zadacha Puankare-Trikomi dlya uravneniya smeshannogo elliptiko-giperbolicheskogo tipa vtorogo roda. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mexanika. 2020. № 65. S. 5-21. DOI 10.17223/19988621/65/1

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