Voloshko L. Models and methods of parameters optimal choosing in boundary value problem for inhomogeneous biharmonic equation

Object of research is boundary value problem for inhomogeneous biharmonic equation for irregulsr domain configuration. Research methods are methods of linear algebra and analitic geometry, mathmetical and functional analyzes, the theory of integral equations, the theory of optimiztion and numerical methods. Research goal is formulation of mathmetical models of parameters optimal choosing in boundary value problem with inhomogeneous biharmonic equation and also to the development and justification of methods and algorithms for solving of these problems. In this work, new models of parameters optimal choosing in boundary value problem with inhomogeneous biharmonic equation have been formulated. Solution existence and uniqueness for all presented problems have been justified. Existence of Freshet derivatives for cost functionals have been proved. Numerical algorithms have been developed for optimal parameters finding in boundary value problem for inhomogeneous biharmonic equation when the shape of domain is irregular. Evaluation of efficiency in developed algorithms has been conducted. Reliability of obtained results and adequacy of the model have been established. Constructed algorithms have been implemented in Borland Delphi 7 environment. Algorithms operations have been demonstrated on different modal problems.