Boundary value problem for a third-order equation wth multiple characteristics

Kurbonov , Odiljon

Innovations in Science and Technologies · 2026-yil

Annotatsiya

This article investigates the well-posedness of a boundary value problem for a class of third-order nonlinear partial differential equations characterized by multiple characteristics. Equations of this type frequently appear in hydrodynamics, plasma physics, and acoustic wave propagation problems, where higher-order dispersion and nonlinear interactions play a decisive role. The primary mathematical objectives of the study are to prove the existence and uniqueness of solutions within appropriate function spaces. An energy method is employed to establish uniqueness. By constructing a suitable energy functional and deriving refined energy estimates, it is shown that the corresponding homogeneous problem possesses only the trivial solution, thereby guaranteeing uniqueness under the prescribed boundary conditions. The method of continuation with respect to a parameter is used to prove existence. Introducing a continuous parameter—which allows the original nonlinear problem to be deformed into a simpler linear analogue with a known solution—enables the establishment of global classical solvability. This approach relies on deriving uniform a priori estimates for the family of parameterized solutions, ensuring that the set of parameters for which the problem is solvable is both open and closed within the parameter space. Furthermore, the interaction between multiple characteristics and nonlinear terms is analyzed in detail, identifying the structural conditions necessary to prevent a loss of solution smoothness. The results presented extend known fundamental existence and uniqueness theorems to a broader class of third-order nonlinear differential equations.

Maqola ma’lumotlari
MualliflarKurbonov , Odiljon
JurnalInnovations in Science and Technologies
NashriyotТошкент давлат иқтисодиёт университети
ISSN3030-3451
Nashr sanasi2026-10-12
Jild3
Son10
Betlar2-11
TilIngliz
Ilmiy sohaIqtisodiyot
Indeksga qo‘shilgan2026-10-13

Maqolaning asl sahifasi

Kalit so‘zlar

Solution, uniqueness, existence, energy integral, nonlinearity, a priori estimate, local solution, parameter, continuation, global solution.

Ilmiy soha

Iqtisodiyot

Iqtibos keltirish

APAKurbonov , Odiljon (2026). BOUNDARY VALUE PROBLEM FOR A THIRD-ORDER EQUATION WTH MULTIPLE CHARACTERISTICS. Innovations in Science and Technologies, 3(10), 2-11. https://innoist.uz/index.php/ist/article/view/1783
GOST (OAK)Kurbonov , Odiljon BOUNDARY VALUE PROBLEM FOR A THIRD-ORDER EQUATION WTH MULTIPLE CHARACTERISTICS // Innovations in Science and Technologies. – 2026. – T. 3, № 10. – P. 2-11.
MLAKurbonov , Odiljon. “BOUNDARY VALUE PROBLEM FOR A THIRD-ORDER EQUATION WTH MULTIPLE CHARACTERISTICS.” Innovations in Science and Technologies, 3(10), 2-11, 2026. https://innoist.uz/index.php/ist/article/view/1783
ChicagoKurbonov , Odiljon. “BOUNDARY VALUE PROBLEM FOR A THIRD-ORDER EQUATION WTH MULTIPLE CHARACTERISTICS.” Innovations in Science and Technologies, 3(10), 2-11 (2026). https://innoist.uz/index.php/ist/article/view/1783
HarvardKurbonov , Odiljon (2026) ‘BOUNDARY VALUE PROBLEM FOR A THIRD-ORDER EQUATION WTH MULTIPLE CHARACTERISTICS’, Innovations in Science and Technologies, 3(10), 2-11. https://innoist.uz/index.php/ist/article/view/1783
BibTeX
@article{kurbonovodiljon2026,
  title = {BOUNDARY VALUE PROBLEM FOR A THIRD-ORDER EQUATION WTH MULTIPLE CHARACTERISTICS},
  author = {Kurbonov , Odiljon},
  journal = {Innovations in Science and Technologies},
  year = {2026},
  volume = {3},
  number = {10},
  pages = {2-11},
  url = {https://innoist.uz/index.php/ist/article/view/1783}
}

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