O‘zbekiston matematika jurnali Volume 69 Issue 4 (2025) · pp. 152-164

An initial-boundary value problem with local and nonlocal conditions for a degenerate partial differential equation of high even order

Karimov, K.T., Oripov, D.D.

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Abstract

In this paper, an initial-boundary value problem with local and nonlocal conditions for a degenerate partial differential equation of high even order in a rectangle is formulated and investigated. The method of energy integrals is used to prove the uniqueness of the solution to the problem, and using spectral analysis methods and the Green function, the solution to the considered problem is constructed as the sum of a Fourier series.

degenerate equation, initial-boundary value problem, method of separation of variables, spectral problem, Green's function method, integral equation, Fourier series

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Cite

APA 7 
Karimov, K.T. & Oripov, D.D. (2025). An initial-boundary value problem with local and nonlocal conditions for a degenerate partial differential equation of high even order. O‘zbekiston matematika jurnali, 69(4), 152-164.
GOST R 7.0.5 
Karimov, K.T., Oripov, D.D. An initial-boundary value problem with local and nonlocal conditions for a degenerate partial differential equation of high even order // O‘zbekiston matematika jurnali. 2025. Т. 69. № 4. С. 152-164.
BibTeX 
@article{k.t.2025,
  author  = {Karimov, K.T. and Oripov, D.D.},
  title   = {An initial-boundary value problem with local and nonlocal conditions for a degenerate partial differential equation of high even order},
  journal = {O‘zbekiston matematika jurnali},
  year    = {2025},
  volume  = {69},
  number  = {4},
  pages   = {152-164}
}
RIS 
TY  - JOUR
AU  - Karimov, K.T.
AU  - Oripov, D.D.
TI  - An initial-boundary value problem with local and nonlocal conditions for a degenerate partial differential equation of high even order
JO  - O‘zbekiston matematika jurnali
PY  - 2025
VL  - 69
IS  - 4
SP  - 152
EP  - 164
ER  -