INTERVAL EXTENSION STRUCTURE BASIC TYPES OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF FORTH ORDER

Abstract

In this article, the interval expansion of the structure of solving basic types of boundary value problems for partial differential equations of the fourth order has been developed. Used Method of R-functions for constructed coordinate sequences. Constructing interval extensions of structural formulas, we consider problems (1) on the transverse bending of thin plates and 5 problems on a plate - rigidly clamped plate, loosely supported plate, elastically fixed plates, partially rigidly clamped and partially elastically fixed plates, plates, partially rigidly clamped and partially free . For the problem, the rigidly clamped plate Formula (7) is an interval structure for solving the boundary value problem (4). Here L={▁ω ▁ψ,ω ̅▁ψ,▁ω ψ ̅,ω ̅ψ ̅ },L_1={▁ω D_1 ▁φ,ω ̅D_1 ▁φ,▁ω D_1 φ ̅,ω ̅D_1 φ ̅ } L_2={▁ω^2 ▁Φ,ω ̅^2 ▁Φ,▁ω^2 Φ ̅,ω ̅^2 Φ ̅ }, [ ▁Φ,Φ ̅ ] is an indefinite interval function. For the free-supported plate problem, a solution is obtained for the interval expansion of the structure in the form (15), (17), [ ▁(Φ_1 ),(Φ_1 ) ̅ ], [ ▁(Φ_2 ),(Φ_2 ) ̅ ]- indefinite interval function, D_2, T_2 - differential operators of the form (11) and (12). For the problem of elastically fixed plates, a solution was obtained in the interval expansion of the structure in the form (21) - (24), [ ▁(Φ_1 ),(Φ_1 ) ̅ ], [ ▁(Φ_2 ),(Φ_2 ) ̅ ]- indefinite interval functions, D_2,T_2,D_1- differential operators of the form (11) and (12), (3). For the problem of partially rigidly clamped and partially elastically fixed plates, a solution was obtained in the interval expansion of the structure in the form of (28), (30), (32), [ ▁(Φ_1 ),(Φ_1 ) ̅ ], [ ▁(Φ_2 ),(Φ_2 ) ̅ ]- indefinite interval functions, D_2,T_2,D_1- differential operators of the form (11) and (12), (6). For the plate problem, partially rigidly pinched and partially free, a solution is obtained in the interval extension of the structure (40), (41), (42), [ ▁(Φ_1 ),(Φ_1 ) ̅ ], [ ▁(Φ_2 ),(Φ_2 ) ̅ ] - indefinite interval functions, D_2,T_2,D_1,D_3- differential operators of the form (11), (12), (6) and (38).