This paper studies an analog of the Tricomi problem for a loaded parabolic-hyperbolic equation of the second kind, which degenerates inside the domain. In proving the existence and uniqueness theorem for a classical solution to the Tricomi-type problem, a general representation of the solution to the loaded parabolic-hyperbolic equation degenerating within the domain is derived. The uniqueness of the solution is established using the extremum principle and the energy integral method. The existence of the solution is equivalently reduced to integral equations of the second kind, specifically Volterra and Fredholm equations, which remain relatively unexplored. Furthermore, a class of prescribed functions is determined to ensure the solvability of the obtained integral equations.
| Mualliflar | Islomov , Bozor, Nasirova , Dildora |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-11-03 |
| Jild | 69 |
| Son | 4 |
| Betlar | 128-140 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-4-13 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-4-13 · Maqolaning asl sahifasi
Second-kind equation, loaded equation, extremum principle, method of energy integrals, Fredholm integral equation of the second kind
| APA | Islomov , Bozor, & Nasirova , Dildora (2025). On a Boundary Value Problem for a Loaded Parabolic-Hyperbolic Equation of the Second Kind Degenerating Inside the Domain. O‘zbekiston matematika jurnali, 69(4), 128-140. https://doi.org/10.29229/uzmj.2025-4-13 |
|---|---|
| GOST (OAK) | Islomov , Bozor, Nasirova , Dildora On a Boundary Value Problem for a Loaded Parabolic-Hyperbolic Equation of the Second Kind Degenerating Inside the Domain // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 4. – P. 128-140. – DOI: 10.29229/uzmj.2025-4-13. |
| MLA | Islomov , Bozor, and Nasirova , Dildora. “On a Boundary Value Problem for a Loaded Parabolic-Hyperbolic Equation of the Second Kind Degenerating Inside the Domain.” O‘zbekiston matematika jurnali, 69(4), 128-140, 2025. https://doi.org/10.29229/uzmj.2025-4-13 |
| Chicago | Islomov , Bozor, and Nasirova , Dildora. “On a Boundary Value Problem for a Loaded Parabolic-Hyperbolic Equation of the Second Kind Degenerating Inside the Domain.” O‘zbekiston matematika jurnali, 69(4), 128-140 (2025). https://doi.org/10.29229/uzmj.2025-4-13 |
| Harvard | Islomov , Bozor, and Nasirova , Dildora (2025) ‘On a Boundary Value Problem for a Loaded Parabolic-Hyperbolic Equation of the Second Kind Degenerating Inside the Domain’, O‘zbekiston matematika jurnali, 69(4), 128-140. https://doi.org/10.29229/uzmj.2025-4-13 |
| BibTeX | @article{islomovbozor2025,
title = {On a Boundary Value Problem for a Loaded Parabolic-Hyperbolic Equation of the Second Kind Degenerating Inside the Domain},
author = {Islomov , Bozor and Nasirova , Dildora},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {4},
pages = {128-140},
doi = {10.29229/uzmj.2025-4-13},
url = {https://doi.org/10.29229/uzmj.2025-4-13}
} |
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