<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">vmait</journal-id><journal-title-group><journal-title xml:lang="ru">Computational Mathematics and Information Technologies</journal-title><trans-title-group xml:lang="en"><trans-title>Computational Mathematics and Information Technologies</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2587-8999</issn><publisher><publisher-name>Донской государственный технический университет</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">vmait-83</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Математическое моделирование процессов эвтрофикации в Азовском море на супер-ЭВМ</article-title><trans-title-group xml:lang="en"><trans-title>Mathematical modeling of eutrophication processes in Azov Sea on supercomputers</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7257-962X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Никитина</surname><given-names>Алла Валерьевна</given-names></name><name name-style="western" xml:lang="en"><surname>Nikitina</surname><given-names>Alla Valerevna</given-names></name></name-alternatives><bio xml:lang="ru"><p>Никитина Алла Валерьевна, доцент кафедры «Интеллектуальные и многопроцессорные системы» Южный федеральный университет (ЮФУ) (РФ, г. Ростов-на-Дону, ул. Б. Садовая, 105/42), доктор технических наук, доцент</p></bio><bio xml:lang="en"><p>Nikitina Alla Valerevna, Associate Professor, Department of intellectual and multiprocessor systems, South state university (SFU) (Bolshaya Sadovaya street, 105/42, Rostov-on-Don, Russian Federation, 344006) Dr.Sci. (Eng.), Associate Professor</p></bio><email xlink:type="simple">nikitina.vm@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9878-0900</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Семенякина</surname><given-names>Алёна Александровна</given-names></name><name name-style="western" xml:lang="en"><surname>Semenyakina</surname><given-names>Alena Aleksandrovna</given-names></name></name-alternatives><bio xml:lang="ru"><p>Семенякина Алёна Александровна, младший научный сотрудник Научно-исследовательского центра супер-ЭВМ и нейрокомпьютеров (РФ, г. Таганрог, пер. Итальянский, д. 106)</p></bio><bio xml:lang="en"><p>Semenyakina Alena Aleksandrovna, Junior researcher, Supercomputers and Neurocomputers Research Center (Italyansky lane, 106, Taganrog, Rostov region, Russian Federation, 347900)</p></bio><email xlink:type="simple">j.a.s.s.y@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Южный федеральный университет (ЮФУ) &#13;
(РФ, г. Ростов-на-Дону, ул. Б. Садовая, 105/42)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>South state university (SFU) &#13;
(Bolshaya Sadovaya street, 105/42, Rostov-on-Don, Russian Federation, 344006)</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Научно-исследовательский центр супер-ЭВМ и нейрокомпьютеров &#13;
(РФ, г. Таганрог, пер. Итальянский, д. 106)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Supercomputers and Neurocomputers Research Center &#13;
(Italyansky lane, 106, Taganrog, Rostov region, Russian Federation, 347900)</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2017</year></pub-date><pub-date pub-type="epub"><day>29</day><month>03</month><year>2023</year></pub-date><volume>1</volume><issue>1</issue><elocation-id>83</elocation-id><permissions><copyright-statement>Copyright &amp;#x00A9; Никитина А.В., Семенякина А.А., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Никитина А.В., Семенякина А.А.</copyright-holder><copyright-holder xml:lang="en">Nikitina A.V., Semenyakina A.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.cmit-journal.ru/jour/article/view/83">https://www.cmit-journal.ru/jour/article/view/83</self-uri><abstract><p>Введение. Статья посвящена исследованию эффективных численных методов решения задачи эвтрофикации вод мелководного водоема с учетом множества факторов, таких, как движение водного потока, пространственно-неравномерное распределение температуры и солености, микротурбулентная диффузия, гравитационное оседание, а также распространение загрязняющих биогенных веществ, кислорода, фито- и зоопланктона и др. Объектом моделирования выступают мелководные водоемы – Азовское море и Таганрогский залив.Материалы и методы. Разработана математическая модель эвтрофикации мелководных водоемов. Параллельная реализация выполнена на основе методов декомпозиции сеточных областей для вычислительно трудоемких задач диффузии-конвекции, учитывающих архитектуру и параметры супер-ЭВМ. Было установлено, что максимальное ускорение достигалось на 128 вычислительных узлах и составило 43 раза. При реализации параллельного алгоритма решения задачи на МВС для распределения данных между процессорами были разработаны два алгоритма, в том числе алгоритм на основе метода k-means, применение которого позволило повысить эффективность алгоритма решения поставленной задачи на 15% по сравнению с алгоритмом, основанном на стандартном разбиении расчетной области.Результаты исследования. Разработаны новые математические модели и программное обеспечение для математического моделирования процессов эвтрофикации мелководных водоемов. Рассчитанные при различных ветровых ситуациях концентрации загрязняющих веществ и планктона принимались к рассмотрению, если относительная погрешность не превышала 30%.С помощью экспедиционных исследований проведена первичная верификация модели экосистемы Азовского моря. Реализована задача моделирования и прогноза состояния водной экосистемы Азовского моря в условиях антропогенного воздействия и всестороннего изучения уникального водного объекта, который в силу мелководности в большей степени подвержен антропогенному влиянию.Создан программный комплекс, объединяющий разработанные математические модели и базы данных, с помощью которого изучены условия, при которых мелководные водоемы подвергаются эвтрофитрованию.Обсуждение и заключения. Решение поставленной задачи водной экологии позволит прогнозировать возможные сценарии изменения качества вод мелководных водоемов, а также изучать механизмы формирования в них зон с пониженным содержанием кислорода.</p></abstract><trans-abstract xml:lang="en"><p>Introduction. The paper is devoted to the research of effective numerical methods for solving eu-trophication problem of shallow waters taking into account water environment, spatially-nonuniform distribution of temperature and salinity, microturbulent diffusion, gravitational sedi-mentation, and spreading of biogenic pollution, oxygen, phyto- and zooplankton, etc. The simula-tion objects are shallow waters – the Azov Sea and Taganrog Bay. Materials and Methods. The mathematical model of eutrophication of shallow waters was devel-oped. Parallel implementation was performed for computationally laborious convection-diffusion problems, taking into account the architecture and parameters of supercomputers based on the de-composition methods of grid domains. We determined that the maximum acceleration was 43 times on 128 computational nodes. We developed two algorithms including the algorithm based on the k-means method for data distribution between processors in parallel implementation. Due to the using these algorithms, the efficiency of algorithm for solving the problem is increased on 15% compared to the algorithm of the standard partition of computational domain. Results. New mathematical models and software complex were developed for mathematical model-ing of eutrophication processes in shallow waters. The concentrations of pollutants and plankton calculated for different wind situations were taken into consideration, if the relative error did not exceed 30%. Due to expedition researches the primary verification of the model of ecosystem of the Azov Sea was performed. The problem of modeling and forecasting the state of water ecosystems of the Azov Sea in conditions of anthropogenic influence and comprehensive research of the unique water ob-ject was implemented. Because of the water object is shallow, it’s more affected by anthropogenic influence. The software complex, combining mathematical models and databases, was designed. Using this complex we researched conditions which are contributed by the eutrophication processes in shallow waters. Discussion and Conclusions. Due to the solving the water ecology problem we can forecast differ-ent scenario of changing the water quality in shallow waters, and to investigate the mechanisms of formation of zones with low oxygen content.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>математическое моделирование</kwd><kwd>эвтрофикация</kwd><kwd>метод минимальных по-правок</kwd><kwd>параллельные вычисления</kwd><kwd>супер-ЭВМ</kwd></kwd-group><kwd-group xml:lang="en"><kwd>mathematical modeling</kwd><kwd>eutrophication</kwd><kwd>minimum corrections method</kwd><kwd>parallel computing</kwd><kwd>supercomputer</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена при поддержке РНФ, проект № 17-11-01286</funding-statement><funding-statement xml:lang="en">This paper was partially supported by the grant No.17-11-01286 of the Russian Science Foundation.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Samarsky, A.A., Nikolaev, E.S. Methods of solving grid equations. Moscow, Science, 1978, pp. 588.</mixed-citation><mixed-citation xml:lang="en">Samarsky, A.A., Nikolaev, E.S. Methods of solving grid equations. Moscow, Science, 1978, pp. 588.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Sukhinov, A.I., Chistyakov, A.E. Adaptive modified alternating triangular iterative method for solving grid equations with non-selfadjoint operator. Mathematical modeling, 2012, vol. 24, no. 1, pp. 3–20.</mixed-citation><mixed-citation xml:lang="en">Sukhinov, A.I., Chistyakov, A.E. Adaptive modified alternating triangular iterative method for solving grid equations with non-selfadjoint operator. Mathematical modeling, 2012, vol. 24, no. 1, pp. 3–20.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">State Research Center "Planeta", available at: http://planet.iitp.ru/english/index_eng.htm.</mixed-citation><mixed-citation xml:lang="en">State Research Center "Planeta", available at: http://planet.iitp.ru/english/index_eng.htm.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Samarsky, A.A. Theory of difference schemes. Moscow, Nauka, 1989.</mixed-citation><mixed-citation xml:lang="en">Samarsky, A.A. Theory of difference schemes. Moscow, Nauka, 1989.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Konovalov, A.N. The method of steepest descent with adaptive alternately-triangular pre-amplification. Differential equations, 2004, vol. 40, no. 7, pp. 953.</mixed-citation><mixed-citation xml:lang="en">Konovalov, A.N. The method of steepest descent with adaptive alternately-triangular pre-amplification. Differential equations, 2004, vol. 40, no. 7, pp. 953.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Konovalov, A.N. The theory of alternating-triangular iterative method. Siberian mathematical journal, 2002, vol. 43, no. 3, pp. 552.</mixed-citation><mixed-citation xml:lang="en">Konovalov, A.N. The theory of alternating-triangular iterative method. Siberian mathematical journal, 2002, vol. 43, no. 3, pp. 552.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Sukhinov, A.I., Chistyakov, A.E., Shishenya, A.V. Error estimate of the solution of the diffusion equation on the basis of the schemes with weights. Mathematical modeling, 2013, vol. 25, no. 11, pp. 53–64.</mixed-citation><mixed-citation xml:lang="en">Sukhinov, A.I., Chistyakov, A.E., Shishenya, A.V. Error estimate of the solution of the diffusion equation on the basis of the schemes with weights. Mathematical modeling, 2013, vol. 25, no. 11, pp. 53–64.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Chetverushkin, B., Gasilov, V., Iakobovski, M., Polyakov, S., Kartasheva, E., Boldarev, A., Abalakin, I., Minkin, A. Unstructured mesh processing in parallel CFD project GIMM. Parallel Computational Fluid Dynamics, Amsterdam, Elsevier, 2005, pp. 501–508.</mixed-citation><mixed-citation xml:lang="en">Chetverushkin, B., Gasilov, V., Iakobovski, M., Polyakov, S., Kartasheva, E., Boldarev, A., Abalakin, I., Minkin, A. Unstructured mesh processing in parallel CFD project GIMM. Parallel Computational Fluid Dynamics, Amsterdam, Elsevier, 2005, pp. 501–508.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Petrov, I.B., Favorsky, A.V., Sannikov, A.V., Kvasov, I.E. Grid-characteristic method using high order interpolation on tetrahedral hierarchical meshes with a multiple time step. Mathematical modeling, 2013, vol. 25, no. 2, pp. 42–52.</mixed-citation><mixed-citation xml:lang="en">Petrov, I.B., Favorsky, A.V., Sannikov, A.V., Kvasov, I.E. Grid-characteristic method using high order interpolation on tetrahedral hierarchical meshes with a multiple time step. Mathematical modeling, 2013, vol. 25, no. 2, pp. 42–52.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Sukhinov, A.I., Chistyakov, A.E., Semenyakina, A.A., Nikitina, A.V. Parallel realization of the tasks of the transport of substances and recovery of the bottom surface on the basis of schemes of high order of accuracy. Computational methods and programming: new computing technology, 2015, vol. 16, no. 2, pp. 256–267.</mixed-citation><mixed-citation xml:lang="en">Sukhinov, A.I., Chistyakov, A.E., Semenyakina, A.A., Nikitina, A.V. Parallel realization of the tasks of the transport of substances and recovery of the bottom surface on the basis of schemes of high order of accuracy. Computational methods and programming: new computing technology, 2015, vol. 16, no. 2, pp. 256–267.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Chistyakov, A.E., Hachunts, D.S., Nikitina, A.V., Protsenko, E.A., Kuznetsova, I.Y. Parallel Library of iterative methods of the SLAE solvers for problem of convection -diffusion-based decomposition in one spatial direction. Modern problems of science and education, 2015, no. 1–1, pp. 1786.</mixed-citation><mixed-citation xml:lang="en">Chistyakov, A.E., Hachunts, D.S., Nikitina, A.V., Protsenko, E.A., Kuznetsova, I.Y. Parallel Library of iterative methods of the SLAE solvers for problem of convection -diffusion-based decomposition in one spatial direction. Modern problems of science and education, 2015, no. 1–1, pp. 1786.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Sukhinov, A.I., Nikitina, A.V., Semenyakina, A.A., Protsenko, E.A. Complex programs and algorithms to calculate sediment transport and multi-component suspensions on a multiprocessor computer system. Engineering journal of Don. 2015, vol. 38, no. 4 (38), pp. 52.</mixed-citation><mixed-citation xml:lang="en">Sukhinov, A.I., Nikitina, A.V., Semenyakina, A.A., Protsenko, E.A. Complex programs and algorithms to calculate sediment transport and multi-component suspensions on a multiprocessor computer system. Engineering journal of Don. 2015, vol. 38, no. 4 (38), pp. 52.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Nikitina, A.V., Abramenko, Y.A., Chistyakov, A.E. Mathematical modeling of oil spill in shallow waters. Informatics, computer science and engineering education, 2015, № 3 (23), pp. 49–55.</mixed-citation><mixed-citation xml:lang="en">Nikitina, A.V., Abramenko, Y.A., Chistyakov, A.E. Mathematical modeling of oil spill in shallow waters. Informatics, computer science and engineering education, 2015, № 3 (23), pp. 49–55.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Chistyakov, A.E., Nikitina, A.V., Ougolnitsky, G.A., Puchkin, V.M., Semenov, I.S., Sukhinov, A.I., Usov, A.B. A differential game model of preventing fish kills in shallow waterbodies. Game Theory and Applications, 2015, vol. 17, pp. 37–48.</mixed-citation><mixed-citation xml:lang="en">Chistyakov, A.E., Nikitina, A.V., Ougolnitsky, G.A., Puchkin, V.M., Semenov, I.S., Sukhinov, A.I., Usov, A.B. A differential game model of preventing fish kills in shallow waterbodies. Game Theory and Applications, 2015, vol. 17, pp. 37–48.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Sukhinov, A.I., Nikitina, A.V., Semenyakina, A.A., Chistyakov, A.E., A set of models, explicit regularized schemes of high order of accuracy and programs for predictive modeling of consequences of emergency oil spill. Parallel computational technologies (PCT ' 2016), proceedings of the international scientific conference, 2016, pp. 308–319.</mixed-citation><mixed-citation xml:lang="en">Sukhinov, A.I., Nikitina, A.V., Semenyakina, A.A., Chistyakov, A.E., A set of models, explicit regularized schemes of high order of accuracy and programs for predictive modeling of consequences of emergency oil spill. Parallel computational technologies (PCT ' 2016), proceedings of the international scientific conference, 2016, pp. 308–319.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Nikitina, A.V., Semenyakina, A.A., Chistyakov, A.E. Parallel implementation of the tasks of diffusion-convection-based schemes of high order of accuracy. Vestnik of computer and information technology, 2016, no. 7 (145), pp. 3–8.</mixed-citation><mixed-citation xml:lang="en">Nikitina, A.V., Semenyakina, A.A., Chistyakov, A.E. Parallel implementation of the tasks of diffusion-convection-based schemes of high order of accuracy. Vestnik of computer and information technology, 2016, no. 7 (145), pp. 3–8.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Sukhinov, A.I., Chistyakov, A.E., Semenyakina, A.A., Nikitina, A.V. Numerical modeling of an ecological condition of the Sea of Azov with application of schemes of the raised accuracy order on the multiprocessor computing system. Computer researches and modeling, 2016, vol. 8, no. 1, pp. 151–168.</mixed-citation><mixed-citation xml:lang="en">Sukhinov, A.I., Chistyakov, A.E., Semenyakina, A.A., Nikitina, A.V. Numerical modeling of an ecological condition of the Sea of Azov with application of schemes of the raised accuracy order on the multiprocessor computing system. Computer researches and modeling, 2016, vol. 8, no. 1, pp. 151–168.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Sukhinov, A.I., Nikitina, A.V., Semenyakina, A.A., Chistyakov, A.E. Complex of models, explicit regularized schemes of high-order of accuracy and applications for predictive modeling of aftermath of emergency oil spill. CEUR Workshop Proceedings. 10th Annual International Scientific Conference on Parallel Computing Technologies, PCT 2016, Arkhangelsk, Russian Federation, 2016, vol. 1576, pp. 308–319.</mixed-citation><mixed-citation xml:lang="en">Sukhinov, A.I., Nikitina, A.V., Semenyakina, A.A., Chistyakov, A.E. Complex of models, explicit regularized schemes of high-order of accuracy and applications for predictive modeling of aftermath of emergency oil spill. CEUR Workshop Proceedings. 10th Annual International Scientific Conference on Parallel Computing Technologies, PCT 2016, Arkhangelsk, Russian Federation, 2016, vol. 1576, pp. 308–319.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Sukhinov, A.I., Nikitina, A.V., Chistyakov, A.E., Semenov, I.S., Semenyakina, A.A., Khachunts, D.S. Mathematical modeling of eutrophication processes in shallow waters on multiprocessor computer system. CEUR Workshop Proceedings. 10th Annual International Scientific Conference on Parallel Computing Technologies, PCT 2016, Arkhangelsk; Russian Federation, 2016, vol. 1576, pp. 320-333.</mixed-citation><mixed-citation xml:lang="en">Sukhinov, A.I., Nikitina, A.V., Chistyakov, A.E., Semenov, I.S., Semenyakina, A.A., Khachunts, D.S. Mathematical modeling of eutrophication processes in shallow waters on multiprocessor computer system. CEUR Workshop Proceedings. 10th Annual International Scientific Conference on Parallel Computing Technologies, PCT 2016, Arkhangelsk; Russian Federation, 2016, vol. 1576, pp. 320-333.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Nikitina, A.V., Sukhinov, A.I., Ougolnitsky, G.A., Usov, A.B., Chistyakov, A.E., Puchkin, M.V., Semenov, I.S. Optimal management of sustainable development at the biological rehabilitation of the Azov Sea. Mathematical modeling, 2016, vol. 28, no. 7, pp. 96–106.</mixed-citation><mixed-citation xml:lang="en">Nikitina, A.V., Sukhinov, A.I., Ougolnitsky, G.A., Usov, A.B., Chistyakov, A.E., Puchkin, M.V., Semenov, I.S. Optimal management of sustainable development at the biological rehabilitation of the Azov Sea. Mathematical modeling, 2016, vol. 28, no. 7, pp. 96–106.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Nikitina, A.V., Sukhinov, A.I., Ougolnitsky, G.A., Usov, A.B., Chistyakov, A.E., Puchkin, M.V., Semenov, I.S. Optimal control of sustainable development in the biological rehabilitation of the Azov Sea. Mathematical Models and Computer Simulations, 2017, no. 9 (1), pp. 101–107.</mixed-citation><mixed-citation xml:lang="en">Nikitina, A.V., Sukhinov, A.I., Ougolnitsky, G.A., Usov, A.B., Chistyakov, A.E., Puchkin, M.V., Semenov, I.S. Optimal control of sustainable development in the biological rehabilitation of the Azov Sea. Mathematical Models and Computer Simulations, 2017, no. 9 (1), pp. 101–107.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
