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Generalized solvability of non-classical boundary-value problems for systems of partial differential equations

https://doi.org/10.25587/2411-9326-2024-3-28-38

Abstract

A brief overview of the authors’ research results on non-classical boundaryvalue problems for linear systems of partial differential equations is given. Some new results in this direction are presented.

About the Authors

B. B. Oshorov
East Siberia State University of Technology and Management
Russian Federation

Bator B. Oshorov

40B Klyuchevskaya Street, Ulan-Ude 670013



E. N. Bulgatova
University of Sanya
China

Elena N. Bulgatova



E. G. Vasilyeva
East Siberia State University of Technology and Management
Russian Federation

Evgenia G. Vasilyeva

40B Klyuchevskaya Street, Ulan-Ude 670013



References

1. Tonelli L., Fondamenti di Calcolo delle Variazioni, Zanichelli, Bologna, vol. 1: 1922; vol. 2: 1923.

2. Sobolev S. L., Some Applications of Functional Analysis in Mathematical Physics, Amer. Math. Soc., Providence, RI (1991).

3. Ladyzhenskaya O. A., Boundary Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).

4. Bitsadze A. V., “On the uniqueness of the solution of the Dirichlet problem for elliptic partial differential equations [in Russian],” Uspekhi Mat. Nauk., 2, No. 6, 211–212 (1948).

5. Vragov V. N., Boundary Value Problems for Non-Classical Equations of Mathematical Physics [in Russian], Novosibisk, Novosib. Gos. Univ. (1983).

6. Oshorov B. B., “Boundary value problems in a strip for an elliptic system [in Russian],” in: Correct Boundary Value Problems for Non-Classical Equations of Mathematical Physics, Collect. Artic., pp. 152–155, Novosibirsk (1980).

7. Oshorov B. B., “On boundary value problems for the Cauchy–Riemann and Bitsadze systems of equations,” Dokl. Math., 407, No. 4, 446–449 (2006).

8. Oshorov B. B. and Oshorov Bato B., “Correct and incorrect boundary value problems for some matrix functions [in Russian],” Vestn. Vost.-Sib. Gos. Tekhnol. Univ., No. 2, 8–16 (2010).

9. Oshorov B. B., “Riemann–Hilbert and Poincare problems with discontinuous boundary conditions for some model systems of partial differential equations,” Differ. Equ., 47, No. 5, 696–705 (2011).

10. Oshorov B. B., Boundary Value Problems with Discontinuous Boundary Conditions for Some Classes of Vector and Matrix Functions [in Russian], Akad. Estestvoznaniya, Moscow (2010).

11. Oshorov Bato B. and Oshorov Bator B., “Boundary value problems for a model system of first-order equations in three-dimensional space,” Differ. Equ., 51, No. 5, 635–641 (2015).

12. Oshorov B. B., “Non-classical boundary value problems for some systems of partial differential equations,” Differ. Equ., 53, No. 6, 789–800 (2017).

13. Oshorov B. B., “Boundary value problems for nonclassical systems of second order differential equations,” J. Math. Sci., 228, No. 4, 421–430 (2018).


Review

For citations:


Oshorov B.B., Bulgatova E.N., Vasilyeva E.G. Generalized solvability of non-classical boundary-value problems for systems of partial differential equations. Mathematical notes of NEFU. 2024;31(3):28-38. (In Russ.) https://doi.org/10.25587/2411-9326-2024-3-28-38

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