Dirichlet boundary value problem for the biharmonic equations with multiple involution
DOI:
https://doi.org/10.70474/b13thr18Keywords:
Dirichlet problem, nonlocal biharmonic equation, multiple involution, integral representation, Green’s functionAbstract
This work studies a Dirichlet boundary value problem for a nonlocal biharmonic equation that includes multiple involutions, meaning the equation depends on values of the unknown function at transformed points. The analysis focuses on whether a solution exists and whether it is unique under appropriate assumptions on the data and operators. Precise conditions are derived that guarantee solvability of the problem. In addition, the solution is expressed in an explicit integral form, which represents the solution using known kernel functions. This representation clarifies the structure of solutions and provides a practical tool for further theoretical analysis and numerical computation applications.
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