Boundary point problem for a system of second-order nonclassical equations

Rakhimov, Doston, Toshpulatov , Murodullo

Techscience.uz - техника фанлари долзарб масалалри · 2025-yil

Annotatsiya

This article studies a boundary value problem for a system of second-order nonclassical equations. The problem is considered together with initial, boundary, and constraint conditions. The solution of the problem is analyzed from the point of view of existence, uniqueness, and conditional stability. Also, an a priori estimate is obtained for the solution and the conditional correctness set of the problem is determined. Based on the definition of J. Adamard, the general ill-posedness of the problem is shown. In addition, in this work, the spectral problem is also analyzed and its eigenvalues and eigenfunctions are determined. It is proved that these eigenfunctions form a Riesz basis, and an approximate solution of the problem is constructed on their basis by the regularization method. The results of the research serve as an important theoretical basis for obtaining stable solutions for ill-posed problems

Maqola ma’lumotlari
MualliflarRakhimov, Doston, Toshpulatov , Murodullo
JurnalTechscience.uz - техника фанлари долзарб масалалри
NashriyotЖиззах политехника институти
ISSN3030-3702, 3030-3702
Nashr sanasi2025-06-11
Jild3
Son2
Betlar18-22
TilIngliz
Ilmiy sohaTexnika
DOI10.47390/ts3030-3702v3i2y2025n03
Indeksga qo‘shilgan2026-08-26

DOI: 10.47390/ts3030-3702v3i2y2025n03 · Maqolaning asl sahifasi

Kalit so‘zlar

system of second-order equations, Irregular problem, Boundary problem, Initial condition, Betting condition, Spectral problem, Eigenvalues, Eigenfunctions, A priori estimate, Conditional correctness, Conditional stability, Regularization method, Riesz basis, Transcendent equation, Positive roots, Functional analysis, Uniqueness of solution, Approximate solution, Equivalent norm, Adamer condition., ikkinchi tartibli tenglamalar sistemasi , Nokorrekt masala , Chegaraviy masala , Boshlang‘ich shart , Tikish sharti , Spektral masala , Xos sonlar , Xos funksiyalar , Aprior baho , Shartli korrektlik , Shartli turg‘unlik , Regulyarlashtirish usuli , Riesz bazisi , Transsendent tenglama , Musbat ildizlar , Funktsional analiz , Yechimning yagonaligi , Taqribiy yechim , Ekvivalent norm , Adamar sharti.

Ilmiy soha

Texnika

Iqtibos keltirish

APARakhimov, Doston, & Toshpulatov , Murodullo (2025). BOUNDARY POINT PROBLEM FOR A SYSTEM OF SECOND-ORDER NONCLASSICAL EQUATIONS. Techscience.uz - техника фанлари долзарб масалалри, 3(2), 18-22. https://doi.org/10.47390/ts3030-3702v3i2y2025n03
GOST (OAK)Rakhimov, Doston, Toshpulatov , Murodullo BOUNDARY POINT PROBLEM FOR A SYSTEM OF SECOND-ORDER NONCLASSICAL EQUATIONS // Techscience.uz - техника фанлари долзарб масалалри. – 2025. – T. 3, № 2. – P. 18-22. – DOI: 10.47390/ts3030-3702v3i2y2025n03.
MLARakhimov, Doston, and Toshpulatov , Murodullo. “BOUNDARY POINT PROBLEM FOR A SYSTEM OF SECOND-ORDER NONCLASSICAL EQUATIONS.” Techscience.uz - техника фанлари долзарб масалалри, 3(2), 18-22, 2025. https://doi.org/10.47390/ts3030-3702v3i2y2025n03
ChicagoRakhimov, Doston, and Toshpulatov , Murodullo. “BOUNDARY POINT PROBLEM FOR A SYSTEM OF SECOND-ORDER NONCLASSICAL EQUATIONS.” Techscience.uz - техника фанлари долзарб масалалри, 3(2), 18-22 (2025). https://doi.org/10.47390/ts3030-3702v3i2y2025n03
HarvardRakhimov, Doston, and Toshpulatov , Murodullo (2025) ‘BOUNDARY POINT PROBLEM FOR A SYSTEM OF SECOND-ORDER NONCLASSICAL EQUATIONS’, Techscience.uz - техника фанлари долзарб масалалри, 3(2), 18-22. https://doi.org/10.47390/ts3030-3702v3i2y2025n03
BibTeX
@article{rakhimovdoston2025,
  title = {BOUNDARY POINT PROBLEM FOR A SYSTEM OF SECOND-ORDER NONCLASSICAL EQUATIONS},
  author = {Rakhimov, Doston and Toshpulatov , Murodullo},
  journal = {Techscience.uz - техника фанлари долзарб масалалри},
  year = {2025},
  volume = {3},
  number = {2},
  pages = {18-22},
  doi = {10.47390/ts3030-3702v3i2y2025n03},
  url = {https://doi.org/10.47390/ts3030-3702v3i2y2025n03}
}

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