{"id":1910,"date":"2022-01-25T10:20:11","date_gmt":"2022-01-25T10:20:11","guid":{"rendered":"https:\/\/akademperiodyka.org.ua\/en\/?p=1910"},"modified":"2026-04-06T13:34:45","modified_gmt":"2026-04-06T13:34:45","slug":"chugunova","status":"publish","type":"post","link":"https:\/\/akademperiodyka.org.ua\/en\/books\/chugunova\/","title":{"rendered":"Mathematical Theory of Higher-Order Degenerate Evolution Models"},"content":{"rendered":"<div class=\"content\">\n<div class=\"field field-name-field-book-project field-type-taxonomy-term-reference field-label-inline clearfix\">\n<div class=\"field-item even\"><strong>Authors:<\/strong><\/div>\n<\/div>\n<div class=\"field field-name-field-book-author field-type-name field-label-inline clearfix\">\n<div class=\"field-item even\">Marina Chugunova<\/div>\n<div class=\"field-item even\">Roman Taranets<\/div>\n<div><\/div>\n<\/div>\n<div class=\"field field-name-field-book-year field-type-number-integer field-label-inline clearfix\">\n<div class=\"field-item even\"><strong>Year:<\/strong> 2019<\/div>\n<\/div>\n<div class=\"field field-name-field-pages field-type-text field-label-inline clearfix\">\n<div class=\"field-item even\"><strong>Pages:<\/strong> 230<\/div>\n<\/div>\n<div class=\"field field-name-field-book-isbn field-type-text field-label-inline clearfix\">\n<div class=\"field-item even\"><strong>ISBN:<\/strong> 978-966-360-382-7<\/div>\n<\/div>\n<div class=\"field field-name-field-book-publication-language field-type-taxonomy-term-reference field-label-inline clearfix\">\n<div class=\"field-item even\"><strong>Publication Language:<\/strong> English<\/div>\n<\/div>\n<div class=\"field field-name-field-book-circulation field-type-number-integer field-label-inline clearfix\">\n<div class=\"field-item even\"><strong>Edition:<\/strong> 200<\/div>\n<\/div>\n<div class=\"field field-name-field-book-publisher field-type-text field-label-inline clearfix\">\n<div class=\"field-item even\"><strong>Publisher:<\/strong> PH &#8220;Akademperiodyka&#8221;<\/div>\n<\/div>\n<div class=\"field field-name-field-book-place-published field-type-text field-label-inline clearfix\">\n<div class=\"field-item even\"><strong>Place Published<\/strong>: Kyiv<\/div>\n<\/div>\n<div class=\"field field-name-field-book-doi field-type-link-field field-label-inline clearfix\">\n<div class=\"field-item even\"><strong>DOI:<\/strong> <a href=\"https:\/\/doi.org\/10.15407\/akademperiodyka.382.230\">https:\/\/doi.org\/10.15407\/akademperiodyka.382.230<\/a><\/div>\n<div><strong>Web of Science Core Collection: <\/strong><a href=\"https:\/\/www.webofscience.com\/wos\/woscc\/full-record\/WOS:001521444200008\">https:\/\/www.webofscience.com\/wos\/woscc\/full-record\/WOS:001521444200008<\/a><\/div>\n<\/div>\n<\/div>\n<div><\/div>\n<div><\/div>\n<div>\n<hr \/>\n<\/div>\n<div class=\"content\">\n<div class=\"field field-name-body field-type-text-with-summary field-label-hidden\">\n<div class=\"field-items\">\n<div class=\"field-item even\">\n<p>This book is devoted to the study of solvability and qualitative behaviour of generalised solutions to initial boundary value problems for high-order nonlinear parabolic equations and systems. The eventual goal of this book is to present with all rigorous details the new applications of energy-entropy methods starting from one-dimensional problems discussed in Chapters 1-3, progressing to an advanced level in considering these methods for thin-film type systems in Chapter 4, 5 and finally showing all the steps of the qualitative analysis for problems in multi-dimensional domains in Chapter 6. While we expect our readers to be familiar with a parabolic PDE theory and also to have some knowledge of classical functional analysis we do not assume any background in non-linear PDE analysis and provide enough details to learn the methods from the book.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a href=\"https:\/\/u-i-n.com.ua\/shop\/matematichna-teoriya-evolyucijnih-modelej-visokogo-poryadku-sho-virodzhuyutsya?variant=468\">You can ordering book in SA \u201cUKRINFORMNAUKA\u201d<\/a><\/p>\n<hr \/>\n<div class=\"content\">\n<div class=\"field field-name-field-references field-type-text-long field-label-above\">\n<div class=\"field-label\"><strong>References:<\/strong><\/div>\n<div class=\"field-items\">\n<div class=\"field-item even\">\n<p class=\"rtejustify\">1. A. Acrivos, B. Jin. Rimming flows within a rotating horizontal cylinder: asymptotic analysis of the thin-film lubrication equations and stability of their solutions. J. Eng. Math., 50: 99-120, 2004.\u00a0<a href=\"https:\/\/doi.org\/10.1007\/s10665-004-1772-7\">https:\/\/doi.org\/10.1007\/s10665-004-1772-7<\/a><\/p>\n<p class=\"rtejustify\">2. N.P. Adhikari and J.L. Goveas. Effects of slip on the viscosity of polymer melts. Journal of Polymer Science Part B: Polymer Physics, 42(10): 1888-1904, 2004.\u00a0<a href=\"https:\/\/doi.org\/10.1002\/polb.20066\">https:\/\/doi.org\/10.1002\/polb.20066<\/a><\/p>\n<p class=\"rtejustify\">3. C. Bandle and H. Brunner. Blowup in diffusion equations: a survey. Journal of Computational and Applied Mathematics, 97(1-2): 3-22, 1998.\u00a0<a href=\"https:\/\/doi.org\/10.1016\/S0377-0427(98)00100-9\">https:\/\/doi.org\/10.1016\/S0377-0427(98)00100-9<\/a><\/p>\n<p class=\"rtejustify\">4. D. Bandyopadhyay, R. Gulabani, and A. Sharma. Instability and dynamics of thin liquid bilayers. Industrial &#038; engineering chemistry research, 44(5): 1259-1272, 2005.\u00a0<a href=\"https:\/\/doi.org\/10.1021\/ie049640r\">https:\/\/doi.org\/10.1021\/ie049640r<\/a><\/p>\n<p class=\"rtejustify\">5. S.G. Bankoff. Stability of liquid flow down a heated inclined plane. Intl. J. Heat Mass Transfer, 14(3): 377-385, 1971.\u00a0<a href=\"https:\/\/doi.org\/10.1016\/0017-9310(71)90157-8\">https:\/\/doi.org\/10.1016\/0017-9310(71)90157-8<\/a><\/p>\n<p class=\"rtejustify\">6. J.W. Barrett and L. El Alaoui. Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants. ESAIM: Mathematical Modelling and Numerical Analysis, 42(05): 749-775, 2008.\u00a0<a href=\"https:\/\/doi.org\/10.1051\/m2an:2008028\">https:\/\/doi.org\/10.1051\/m2an:2008028<\/a><\/p>\n<p class=\"rtejustify\">7. J.W. Barrett, H. Garcke, R. N\u00a8urnberg. Finite element approximation of surfactant spreading on a thin film. SIAM J. Numer. Anal., 41(4): 1427-1464, 2003.\u00a0<a href=\"https:\/\/doi.org\/10.1137\/S003614290139799X\">https:\/\/doi.org\/10.1137\/S003614290139799X<\/a><\/p>\n<p class=\"rtejustify\">8. J.W. Barrett, R. N\u00a8urnberg. Convergence of a finite-element approximation of surfactant spreading on a thin film in the presence of van der Waals forces. IMA Journal of Numerical Analysis, 24(2): 323-363, 2004.\u00a0<a href=\"https:\/\/doi.org\/10.1093\/imanum\/24.2.323\">https:\/\/doi.org\/10.1093\/imanum\/24.2.323<\/a><\/p>\n<p class=\"rtejustify\">9. E.S. Benilov, M.S. Benilov, and N. Kopteva. Steady rimming flows with surface tension. J. Fluid Mech., 597: 91-118, 2008.\u00a0<a href=\"https:\/\/doi.org\/10.1017\/S0022112007009585\">https:\/\/doi.org\/10.1017\/S0022112007009585<\/a><\/p>\n<p class=\"rtejustify\">10. E.S. Benilov, S.B.G. O&#8217;Brien, and I.A. Sazonov. A new type of instability: explosive disturbances in a liquid film inside a rotating horizontal cylinder. J. Fluid Mech., 497: 201-224, 2003.\u00a0<a href=\"https:\/\/doi.org\/10.1017\/S0022112003006633\">https:\/\/doi.org\/10.1017\/S0022112003006633<\/a><\/p>\n<p class=\"rtejustify\">11. T.B. Benjamin. Wave formation in laminar flow down an inclined plane. J. Fluid Mech., 2(06): 554-573, 1957.\u00a0<a href=\"https:\/\/doi.org\/10.1017\/S0022112057000373\">https:\/\/doi.org\/10.1017\/S0022112057000373<\/a><\/p>\n<p class=\"rtejustify\">12. E. Beretta. Selfsimilar source solutions of a fourth order degenerate parabolic equation. Nonlinear Anal., 29(7): 741-760, 1997.\u00a0<a href=\"https:\/\/doi.org\/10.1016\/S0362-546X(97)81321-1\">https:\/\/doi.org\/10.1016\/S0362-546X(97)81321-1<\/a><\/p>\n<p class=\"rtejustify\">13. E. Beretta, M. Bertsch, and R. Dal Passo. Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation. Arch. Rational Mech. Anal., 129(2): 175-200, 1995. 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Nonlinear Anal., 18: 217-234, 1992.\u00a0<a href=\"https:\/\/doi.org\/10.1016\/0362-546X(92)90060-R\">https:\/\/doi.org\/10.1016\/0362-546X(92)90060-R<\/a><\/p>\n<p class=\"rtejustify\">18. A.J. Bernoff. personal communication, 1998.\u00a0<a href=\"https:\/\/doi.org\/10.1016\/S1361-3723(98)80020-1\">https:\/\/doi.org\/10.1016\/S1361-3723(98)80020-1<\/a><\/p>\n<p class=\"rtejustify\">19. A.L. Bertozzi and A.J. Bernoff. Singularities in a modified KuramotoSivashinsky equation describing interface motion for phase transition. Physica D. Nonlinear Phenomena, 85(3): 375-404, 1995.\u00a0<a href=\"https:\/\/doi.org\/10.1016\/0167-2789(95)00054-8\">https:\/\/doi.org\/10.1016\/0167-2789(95)00054-8<\/a><\/p>\n<p class=\"rtejustify\">20. A.L. Bertozzi, G. Gr\u00a8un, and T.P. Witelski. Dewetting films: bifurcations and concentrations. 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Long-wave instabilities and saturation in thin film equations. Comm. Pur. Appl. Math., 51(6): 625-651, 1998.\u00a0<a href=\"https:\/\/doi.org\/10.1002\/(SICI)1097-0312(199806)51:6%3c625::AID-CPA3%3e3.0.CO;2-9\">https:\/\/doi.org\/10.1002\/(SICI)1097-0312(199806)51:6<625::AID-CPA3>3.0.CO;2-9<\/a><\/p>\n<p class=\"rtejustify\">24. A.L. Bertozzi and M.C. Pugh. Finite-time blow-up of solutions of some long-wave unstable thin film equations. Indiana Univ. Mathematics J., 49(4): 1323-1366, 2000.\u00a0<a href=\"https:\/\/doi.org\/10.1512\/iumj.2000.49.1887\">https:\/\/doi.org\/10.1512\/iumj.2000.49.1887<\/a><\/p>\n<p class=\"rtejustify\">25. A.L. Bertozzi, M.P. Brenner, T.F. Dupont, and L.P. Kadanoff. Singularities and similarities in interface flows. In Trends and perspectives in applied mathematics, volume 100 of Appl. Math. Sci., 155-208. 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Journal of rheology, 46(1): 145-167, 2002.\u00a0<a href=\"https:\/\/doi.org\/10.1122\/1.1427912\">https:\/\/doi.org\/10.1122\/1.1427912<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Authors: Marina Chugunova Roman Taranets Year: 2019 Pages: 230 ISBN: 978-966-360-382-7 Publication Language: English Edition: 200 Publisher: PH &#8220;Akademperiodyka&#8221; Place Published: Kyiv DOI: https:\/\/doi.org\/10.15407\/akademperiodyka.382.230 Web of Science Core Collection: https:\/\/www.webofscience.com\/wos\/woscc\/full-record\/WOS:001521444200008 This book is devoted to the study of solvability and qualitative behaviour of generalised solutions to initial boundary value problems for high-order nonlinear parabolic equations [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1912,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,21,24],"tags":[],"class_list":["post-1910","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-books","category-scientific_monographs","category-ukrainian_scientifical_book"],"_links":{"self":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/1910","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/comments?post=1910"}],"version-history":[{"count":11,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/1910\/revisions"}],"predecessor-version":[{"id":7841,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/1910\/revisions\/7841"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/media\/1912"}],"wp:attachment":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/media?parent=1910"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/categories?post=1910"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/tags?post=1910"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}