2024-03-29T12:42:11Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696842022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116OPTIMAL CONTROL OF A SINGULAR DIFFUSION EQUATION WITH CONSTRAINTOhtsuka, TakeshiShirakawa, KenYamazaki, Noriaki410In this paper, we consider an optimal control problem for a state problem of a one dimensional Allen-Cahn type equation, which is derived from a free energy including the total variation interfacial energy and the constraint by the indicator function. So, the state problem contains the singular diffusion coming from the total variation, and another singular term coming from the constraint. The main conclusions of this paper are concerned with the existence of an optimal control (optimal pair) and the necessary condition (optimality condition) of an optimal pair. Furthermore, the analytic methods, performed in this paper, will provide an effective approximating approach to the optimal pairs of our control problem.Othersapplication/pdfhttp://hdl.handle.net/2115/69684https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69684/1/pre875d.pdfHokkaido University Preprint Series in Mathematics8752007engpublisher