{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:27:11Z","timestamp":1775053631703,"version":"3.50.1"},"reference-count":4,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["17-01-00074"],"award-info":[{"award-number":["17-01-00074"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Bioinform. Comput. Biol."],"published-print":{"date-parts":[[2019,2]]},"abstract":"<jats:p> In this paper, a problem of chemotherapy of a malignant tumor is considered. Dynamics is piecewise monotone and a therapy function has two maxima. The aim of therapy is to minimize the number of tumor cells at the given final instance. <\/jats:p><jats:p> The main result of this work is the construction of optimal feedbacks in the chemotherapy task. The construction of optimal feedback is based on the value function in the corresponding problem of optimal control (therapy). The value function is represented as a minimax generalized solution of the Hamilton\u2013Jacobi\u2013Bellman equation. It is proved that optimal feedback is a discontinuous function and the line of discontinuity satisfies the Rankin\u2013Hugoniot conditions. Other results of the work are illustrative numerical examples of the construction of optimal feedbacks and Rankin\u2013Hugoniot lines. <\/jats:p>","DOI":"10.1142\/s0219720019400043","type":"journal-article","created":{"date-parts":[[2019,2,13]],"date-time":"2019-02-13T01:30:53Z","timestamp":1550021453000},"page":"1940004","source":"Crossref","is-referenced-by-count":3,"title":["Numerical constructions of optimal feedback in models of chemotherapy of a malignant tumor"],"prefix":"10.1142","volume":"17","author":[{"given":"Natalia G.","family":"Novoselova","sequence":"first","affiliation":[{"name":"N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences (IMM UB RAS), 16 S. Kovalevskaya Str., Yekaterinburg 620990, Russia"},{"name":"Ural Federal University Named After the First President of Russia B. N. Yeltsin, 19 Mira Str., Yekaterinburg 620002, Russia"}]}],"member":"219","published-online":{"date-parts":[[2019,3,14]]},"reference":[{"key":"S0219720019400043BIB001","doi-asserted-by":"publisher","DOI":"10.1134\/S096554250806002X"},{"issue":"4","key":"S0219720019400043BIB002","first-page":"265","volume":"23","author":"Subbotina NN","year":"2017","journal-title":"J \u201cProceedings of the Institute of Mathematics and Mechanics\u201d"},{"key":"S0219720019400043BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0847-1"},{"key":"S0219720019400043BIB004","series-title":"Faculty of Mechanics and Mathematics","volume-title":"First-Order Partial Differential Equations (Study Guide)","author":"Goritskiy AY","year":"1999"}],"container-title":["Journal of Bioinformatics and Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219720019400043","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,23]],"date-time":"2019-09-23T22:40:55Z","timestamp":1569278455000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219720019400043"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2]]},"references-count":4,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2019,3,14]]},"published-print":{"date-parts":[[2019,2]]}},"alternative-id":["10.1142\/S0219720019400043"],"URL":"https:\/\/doi.org\/10.1142\/s0219720019400043","relation":{},"ISSN":["0219-7200","1757-6334"],"issn-type":[{"value":"0219-7200","type":"print"},{"value":"1757-6334","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2]]}}}