Optimization of the boundary conditions of an inhomogeneous biharmonic equation

Mathematical model construction of complicate physical phenomenon often leads to the setting and solving problems of parameters optimal control in differential equations in partial derivatives. Chosen equation with boundary and initial conditions is usually mathematical model basis of the object, which is under analysis. Optimal control of right-hand side function in non-linear problem for inhomogeneous biharmonic has been investigated. With the help of various gradient methods the problems of parameters control in such equations are solved successfully. Herewith linear problem is solved with the potential method on every step. In this work biharmonic potentials with logarithmic singularity are under consideration. That is why parameters optimization in these problems are conducted together with elimination of their incorrectness. It should be noted that system optimal control problems, described with biharmonic equations in irregular shape region, are studied poorly. Therefore the object of investigation is one of boundary conditions for inhomogeneous biharmonic equation. The circumstance which complicated the problem was irregularity of function domain. Clearly that this problem can be solved with computational mathematics methods. Without precise solution of linear problem, it is impossible to use gradient method, build converging iterative process, and obtain precise solution of optimization problem. Algorithm for linear boundary value problem solution with boundary integral equations overcomes this problem successfully. Physical examples of numerical implementation have been presented, analysis of obtained solutions have been conducted. Their accuracy, algorithm simplicity and time spent evidence about this approach promising for practical results obtaining in plate theory and mathematical physics problems successful numerical solving