On a boundary value problem for the biharmonic equation

2015 ◽  
Author(s):  
Tynysbek Sh. Kal’menov ◽  
Ulzada A. Iskakova
Keyword(s):  
Boundary Value Problem ◽  
Biharmonic Equation ◽  
Boundary Value

scholarly journals Biharmonic Equation on Annulus in a Unit Sphere with Polynomial Boundary Condition

2017 ◽  
Vol 13 (1) ◽  
pp. 51
Author(s):  
Ikhsan Maulidi ◽  
Agah D Garnadi
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Unit Sphere ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Boundary Function ◽  
Exact Algorithms ◽  
Polynomial Functions ◽  
Dirichlet Conditions ◽  
Laplace Equations

We studied Biharmonic boundary value problem on annulus with polynomial data. We utilize an exact algorithms for solving Laplace equations with Dirichlet conditions with polynomial functions data. The algorithm requires differentiation of the boundary function, but no integration.

scholarly journals On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2020
Author(s):  
Batirkhan Turmetov ◽  
Valery Karachik ◽  
Moldir Muratbekova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Boundary Operator ◽  
Biharmonic Operator ◽  
Uniqueness Of Solutions ◽  
Neumann Type ◽  
Type Boundary

A nonlocal analogue of the biharmonic operator with involution-type transformations was considered. For the corresponding biharmonic equation with involution, we investigated the solvability of boundary value problems with a fractional-order boundary operator having a derivative of the Hadamard-type. First, transformations of the involution type were considered. The properties of the matrices of these transformations were investigated. As applications of the considered transformations, the questions about the solvability of a boundary value problem for a nonlocal biharmonic equation were studied. Modified Hadamard derivatives were considered as the boundary operator. The considered problems covered the Dirichlet and Neumann-type boundary conditions. Theorems on the existence and uniqueness of solutions to the studied problems were proven.

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