Classical solvability of the mixed problem for a integro-differential equation with the square of the Barenblatt-Zheltov-Kochina operator
Kvadrati bilan berilgan Barenblatt-Jeltov-Kochina operatori qatnashgan integro-differentsial tenglama uchun aralash masalaning klassik yechilishi
Raxmonov F. Tankeeva A.
2024Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan
Bulletin of the Institute of Mathematics
2024#7Issue 194 - 102 pp.
In the present paper, the unique classical solvability and the construction of the solution of mixed problems for a nonlinear integro-differential equation involving the square of the Barenblatt-Zheltov-Kochina operator have been studied. The method of Fourier series based on the separation of variables is used. A countable system of nonlinear integral equations is obtained. Sufficient coefficient conditions for the unique regular solvability of the mixed problem are established. The method of successive approximations combined with the method of compressing mapping are applied.
fourth order equation , Mixed problem , nonlinear integro-differential equation , regular solvability , square of the Barenblatt-Zheltov-Kochina operator
Text of the article Перейти на текст статьи
National University of Uzbekistan, Uzbekistan
Aktobe regional university, Kazakhstan
National University of Uzbekistan
Aktobe regional university
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026