caa a22 4500 378854275 CHVBK 20180305123331.0 cr unu---uuuuu 161128e20031201xx s 000 0 eng 10.1515/156939403770888255 doi (NATIONALLICENCE)gruyter-10.1515/156939403770888255 Serovajsky S. Ya Al-Farabi Kazakh National University, al-Farabi ave., 71, Almaty, 480078, Kazakhstan. E-mail: serovajskys@mail.ru Sequential extension in the problem of control in coefficients for elliptic-type equations [Elektronische Daten] [S. Ya. Serovajsky] The problem of control in coefficients for the elliptic-type equation is considered. For this problem, set by Lions [1], it is not too difficult a matter to obtain necessary optimality conditions under the assumption that the optimal control does exist; yet, solvability of this problem is hard to establish. Nonetheless, it makes sense to search for an admissible control such that the value of the functional calculated on this control is as close as is wished to its lower bound. In this paper, a method for finding minimizing sequences is proposed. The approach used is based on sequential extension of the problem which is analogous to the scheme of complement of spaces [2]. For the extended problem, necessary conditions for sequential optimum property, which characterize minimizing sequences, are established. With the example of Varga [3], we show that, following this method, one can find the minimizing sequences even if the optimal control does not exist. Copyright 2003, Walter de Gruyter Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/5(2003-12-01), 523-536 0928-0219 11:5<523 2003 11 jiip https://doi.org/10.1515/156939403770888255 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939403770888255 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Serovajsky S. Ya Al-Farabi Kazakh National University, al-Farabi ave., 71, Almaty, 480078, Kazakhstan. E-mail: serovajskys@mail.ru NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/5(2003-12-01), 523-536 0928-0219 11:5<523 2003 11 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter