We present a boundary optimal control approach for a Bernoulli free boundary problem. Our control objective consists in tracking a free boundary to an a priori given desired one. An appropriate cost functional is chosen for this purpose and its gradient is analytically derived. The resulting optimality conditions are discretized and the minimization problem is solved numerically by a steepest d...

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

The vibro-acoustic characteristics of cylindrical shell are widely studied because of its strong engineering application background, especially when the shell is immersed in infinite fluid field or partially immersed. In the present paper, the method for analyzing sound radiation of semi-submerged finite cylindrical shell with antisymmetric velocity distribution is first proposed. The orthogona...

The main aim of this article is to analyze mixed finite element method for the second order Dirichlet boundary control problem. We develop both a priori and posteriori error analysis using energy space based approach. obtain optimal estimates in norm L2-norm with help auxiliary problems. reliability efficiency proposed estimator discussed Helmholtz decomposition. Numerical experiments are prese...

The recent progress of physiological measurement allows us to observe membrane potential behaviors of extensive regions with higher spatial and temporal resolutions. Accordingly, a new theory has been expected with which we can analyze the spatiotemporal dynamics of the membrane potential with the cell-shape and the spatial distributions of electrical parameters taken into consideration quantit...