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<article 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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Contemporary Mathematics. Fundamental Directions</journal-id><journal-title-group><journal-title xml:lang="en">Contemporary Mathematics. Fundamental Directions</journal-title><trans-title-group xml:lang="ru"><trans-title>Современная математика. Фундаментальные направления</trans-title></trans-title-group></journal-title-group><issn publication-format="print">2413-3639</issn><issn publication-format="electronic">2949-0618</issn><publisher><publisher-name xml:lang="en">Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">22264</article-id><article-id pub-id-type="doi">10.22363/2413-3639-2018-64-1-98-130</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>New Results</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Новые результаты</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Some Free Boundary Problems Arising in Rock Mechanics</article-title><trans-title-group xml:lang="ru"><trans-title>Несколько задач со свободной границей, возникающих в механике горных пород</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Meirmanov</surname><given-names>A M</given-names></name><name xml:lang="ru"><surname>Мейрманов</surname><given-names>А М</given-names></name></name-alternatives><email>anvarbek@list.ru</email><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Galtsev</surname><given-names>O V</given-names></name><name xml:lang="ru"><surname>Гальцев</surname><given-names>О В</given-names></name></name-alternatives><email>galtsev_o@bsu.edu.ru</email><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Galtseva</surname><given-names>O A</given-names></name><name xml:lang="ru"><surname>Гальцева</surname><given-names>О А</given-names></name></name-alternatives><email>galtseva@bsu.edu.ru</email><xref ref-type="aff" rid="aff2"/></contrib></contrib-group><aff id="aff1"><institution>Yachay Tech University</institution></aff><aff-alternatives id="aff2"><aff><institution xml:lang="en">Belgorod State University</institution></aff><aff><institution xml:lang="ru">Белгородский государственный университет</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2018-12-15" publication-format="electronic"><day>15</day><month>12</month><year>2018</year></pub-date><volume>64</volume><issue>1</issue><issue-title xml:lang="en">Diﬀerential and Functional Diﬀerential Equations</issue-title><issue-title xml:lang="ru">Дифференциальные и функционально-дифференциальные уравнения</issue-title><fpage>98</fpage><lpage>130</lpage><history><date date-type="received" iso-8601-date="2019-11-29"><day>29</day><month>11</month><year>2019</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2019, Contemporary Mathematics. Fundamental Directions</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2019, Современная математика. Фундаментальные направления</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="en">Contemporary Mathematics. Fundamental Directions</copyright-holder><copyright-holder xml:lang="ru">Современная математика. Фундаментальные направления</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/></permissions><self-uri xlink:href="https://journals.rudn.ru/CMFD/article/view/22264">https://journals.rudn.ru/CMFD/article/view/22264</self-uri><abstract xml:lang="ru">В этой статье мы рассматриваем несколько физических процессов в механике горных пород, которые описываются задачами со свободной границей. 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