BOUNDARY VALUE PROBLEMS WITH AN INTEGRO-DIFFERENTIAL NON-LOCAL CONDITION FOR COMPOSITE TYPE DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER

С ИНТЕГРО-ДИФФЕРЕНЦИАЛЬНЫМ НЕЛОКАЛЬНЫМ УСЛОВИЕМ ДЛЯ ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ СОСТАВНОГО ТИПА ЧЕТВЁРТОГО ПОРЯДКА
Kozhanov A.I. Kenzhebay Kh.
2023 Chelyabinsk State University

Chelyabinsk Physical and Mathematical Journal
2023 #8 Issue 4 516 - 527 pp.

The paper studies new nonlocal boundary value problems with an integro-differential boundary condition for unsteady differential equations of the Sobolev type of the fourth order. The peculiarity of the studied problems is that they contain derivatives both in spatial variables and derivatives in time variables in the boundary condition. For the problems under study, the existence and uniqueness theorems of regular solutions are proved – solutions having all derivatives generalized by S.L. Sobolev included in the corresponding equations.

composite type equation , integro-differential boundary conditions , nonlocal problem , regular solution , Sobolev type equation , solution existence , solution uniqueness

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Sobolev Institute of Mathematics of Siberian Branch of RAS, Novosibirsk, Russian Federation
al-Farabi Kazakh National University, Almaty, Kazakhstan

Sobolev Institute of Mathematics of Siberian Branch of RAS
al-Farabi Kazakh National University

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