In the process of studying mixed-type loaded equations, it is impossible to directly apply the existing extremum principles and existence theorems, as well as the methods of classical theory. This is primarily due to the lack of a general solution for such equations; on the other hand, such problems are reduced to poorly studied integral equations with displacements. It should be noted that boundary value problems for loaded equations with a second-order perturbation line have not been studied to the present day. In this article, boundary value problems given by Gellerstedt conditions in parallel characteristics for loaded parabolic-hyperbolic equations with a second-order perturbation line are studied. The uniqueness of the problems is proved using the energy integrals and the extremum principle, which are not studied for parabolic-hyperbolic equations, and the existence is proved using the method of integral equations.
| Mualliflar | B.I. Islomov, D.A. Nasirova |
|---|---|
| Jurnal | Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi |
| Nashriyot | Самарқанд давлат университети |
| ISSN | 2091-5446, 2181-1296 |
| Nashr sanasi | 2025-06-01 |
| Jild | 5 |
| Son | 1 |
| Betlar | 22-32 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.59251/2181-3973.2025.v1.138.1.3572 |
| Indeksga qo‘shilgan | 2026-09-02 |
DOI: 10.59251/2181-3973.2025.v1.138.1.3572 · Maqolaning asl sahifasi
| APA | B.I. Islomov, & D.A. Nasirova (2025). BOUNDARY VALUE PROBLEMS WITH GELLERSTEDT CONDITIONS ON PARALLEL CHARACTERISTICS FOR A LOADED EQUATION OF THE SECOND-KIND PARABOLIC–HYPERBOLIC TYPE DEGENERATING INSIDE THE DOMAIN. Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(1), 22-32. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3572 |
|---|---|
| GOST (OAK) | B.I. Islomov, D.A. Nasirova BOUNDARY VALUE PROBLEMS WITH GELLERSTEDT CONDITIONS ON PARALLEL CHARACTERISTICS FOR A LOADED EQUATION OF THE SECOND-KIND PARABOLIC–HYPERBOLIC TYPE DEGENERATING INSIDE THE DOMAIN // Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi. – 2025. – T. 5, № 1. – P. 22-32. – DOI: 10.59251/2181-3973.2025.v1.138.1.3572. |
| MLA | B.I. Islomov, and D.A. Nasirova. “BOUNDARY VALUE PROBLEMS WITH GELLERSTEDT CONDITIONS ON PARALLEL CHARACTERISTICS FOR A LOADED EQUATION OF THE SECOND-KIND PARABOLIC–HYPERBOLIC TYPE DEGENERATING INSIDE THE DOMAIN.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(1), 22-32, 2025. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3572 |
| Chicago | B.I. Islomov, and D.A. Nasirova. “BOUNDARY VALUE PROBLEMS WITH GELLERSTEDT CONDITIONS ON PARALLEL CHARACTERISTICS FOR A LOADED EQUATION OF THE SECOND-KIND PARABOLIC–HYPERBOLIC TYPE DEGENERATING INSIDE THE DOMAIN.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(1), 22-32 (2025). https://doi.org/10.59251/2181-3973.2025.v1.138.1.3572 |
| Harvard | B.I. Islomov, and D.A. Nasirova (2025) ‘BOUNDARY VALUE PROBLEMS WITH GELLERSTEDT CONDITIONS ON PARALLEL CHARACTERISTICS FOR A LOADED EQUATION OF THE SECOND-KIND PARABOLIC–HYPERBOLIC TYPE DEGENERATING INSIDE THE DOMAIN’, Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(1), 22-32. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3572 |
| BibTeX | @article{biislomov2025,
title = {BOUNDARY VALUE PROBLEMS WITH GELLERSTEDT CONDITIONS ON PARALLEL CHARACTERISTICS FOR A LOADED EQUATION OF THE SECOND-KIND PARABOLIC–HYPERBOLIC TYPE DEGENERATING INSIDE THE DOMAIN},
author = {B.I. Islomov and D.A. Nasirova},
journal = {Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi},
year = {2025},
volume = {5},
number = {1},
pages = {22-32},
doi = {10.59251/2181-3973.2025.v1.138.1.3572},
url = {https://doi.org/10.59251/2181-3973.2025.v1.138.1.3572}
} |
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