A Linearization Technique for Optimal Design of the Damping Set with Internal Dissipation
نویسندگان
1 Department of Mathematics, Faculty of Mathematics, Shiraz University of Technology, Shiraz, Iran.
2 Department of Mathematics, Jahrom University, Jahrom, Iran, P. O. Box: 74135-111 Dept. of Mathematics, Shiraz University of Technology, Shiraz , Iran.
3 Department of Mathematics, Faculty of Mathematics, Shiraz University of Technology, Shiraz, Iran.
doi
10.22067/ijnao.v6i1.44335چکیده
Considering a damped wave system defined on a two-dimensional domain, with a dissipative term localized in an unknown subset with an unknown damping parameter, we address the shape design ill-posed problem which consists of optimizing the shape of the unknown subset in order to minimize the energy of the system at a given time. By using a new approach based on the embedding process, first, the system is formulated in variational form; then, by transferring the problem into polar coordinates and defining two positive Radon measures, we represent the problem in a space of measures. In this way, the shape design problem is changed into an infinite linear one whose solution is guaranteed. In this stage, by applying two subsequent approximation steps, the optimal solution (optimal control, optimal region, optimal damping parameter and optimal energy) is identified by a three-phase optimization search technique. Numerical simulations are also given in order to compare this new method with another one.
