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On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions
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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.
Title: On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions
Description:
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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